Category: Chemistry
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Continuous Spectrum: Definition, Types, and Examples
Continue ReadingContinuous Spectrum
A spectrum is defined as a set of wavelengths that is a characteristic of electromagnetic radiation which is produced or absorbed by a specific object, substance, atom, or molecule. The colors of the rainbow, infrared radiation, ultraviolet radiation, and x-ray are few examples of the same.
Typically, there are two individual classes of spectra:
i. Continuous Spectrum
ii. Discrete Spectrum
Continuous Spectrum Definition
For a continuous spectrum, the light is generally composed of a wide, continuous range of colors (or energies) but with discrete spectra, only bright or dark lines at very discrete and sharply defined colors (energies) are observed. Discrete spectra are further divided into 2 spectrums; Emission spectra and absorption spectra.
Discrete Spectra
There are two forms of discrete spectra: emission spectrum ( or bright-line spectra) and absorption spectrum(or dark line spectra).
Emission Spectrum: When electromagnetic radiation interacts with atoms and molecules of matter, then the electrons present in these atoms absorb energy and move to a higher energy state, thus losing their stability. Now, to regain their stability, the electrons move from the higher energy state to their lower energy state. Thus, to complete this job, these atoms and molecules produce radiation in several regions of the electromagnetic spectrum. This spectrum of radiation produced by electrons in the excited state of atoms or molecules is termed as an emission spectrum.
Absorption Spectra: When a ray of white light falls on a prism it generally experiences refraction twice. First, when it travels from the rarer medium (that is air) to a denser medium (that is glass) and then again from the denser medium ( example; glass) to a rarer medium (example; air). Lastly, a band of colors called a spectrum is observed.
On observing this spectrum more thoroughly, it was found that the color having a smaller wavelength deviates the most and vice versa. Thus, a spectrum of colors ranging from red to violet is detected where the colour red has the longest wavelength and thus suffers the least deviation. This kind of spectrum formed is termed as a continuous spectrum.
How is a Continuous Spectrum Produced?
When Newton performed his famous experiment with a prism and sunlight, he observed that the Sun formed a “rainbow” of colors. This is called as a continuous spectrum. Therefore, light from the Sun, and any star, forms a continuous spectrum.
For example; The light produced by incandescent light bulbs is an example of a continuous spectrum. These types of bulbs give off light by using a very thin coil of metal, the filament, (generally tungsten).
The Chemistry Of Continuous Spectrum
To fully understand continuous spectrum chemistry, it is significant to study the electromagnetic spectrum. White light is a continuous spectrum but this is only a part of a larger electromagnetic spectrum which further comprises of radio waves, infrared rays, microwaves, ultraviolet, gamma rays, and x-rays.
Even the sun’s light is believed to be continuous since rainbows are observed after it rains. There are often gaps where nothing is visible when the light is examined in detail through a spectrometer. A truly continuous spectrum should not contain any gaps and finding gaps in the sun’s light is how researchers know what it is made of.
Continuous Spectrum Examples
Rainbow is commonly accepted as an example as it details all the colors (or wavelengths) from red to violet without any gaps. Though, the sun’s light is not an ideal example of a continuous spectrum as it often contains absorption gaps. A perfect example of a continuous spectrum can be shown when a ray of white light is passed through a prism in suitable lab environments. Other researchers have shown that heating up objects till they glow can also produce the spectrum. This is because atoms or molecules produce white light at glowing.
To produce a complete continuous spectrum, absorption and emission spectra are put together. An emission spectrum is the exact opposite of an absorption spectrum. An absorption spectrum displays a few wavelengths with certain colors missing whereas an emission spectrum only displays the colors which are missing in an absorption spectrum. Therefore, combining the two spectra would give us all the wavelengths that are required to form a continuous spectrum.
Continuous Spectrum vs Line Spectrum
The continuous spectrum contains no gaps however the line spectrum contains several gaps. both absorption and emission spectra are responsible for creating continuous and line spectra. The main difference between these two spectra is that continuous spectra have all the wavelengths whereas line spectrum contains only some of the wavelengths. Line spectrum can be produced in emission and absorption spectrum whereas continuous spectrum occurs only when both the spectra that is absorption and emission spectra of a single species are put together.
Continuous Spectrum Examples
Q1. A continuous spectrum is formed by which of the following;
A. Incandescent electric bulb
B. Sun
C. Hydrogen molecules
D. Sodium vapor lamp
A continuous spectrum is referred to as a beam of light in which all the wavelengths are present within a given limit. A continuous spectrum is primarily formed by thermal emission from a blackbody. Only certain wavelengths can be produced and absorbed by the atom when the energy levels in the atom are quantized. This can be further explained by Bohr’s Quantization Principle.
The sunlight and Incandescent light can produce a continuous spectrum as it mainly contains the photodissociation of hydride ions (or negatively charged hydrogen atoms). There are several ways by which a continuous spectrum is formed such as when a ray of white light is incident on a prism, a band of seven colors is observed or a rainbow formed in sunlight, however, heating of gas forms an emission spectrum as the gas molecules absorb heat energy and produce it in the surrounding.
Hence, options A and B are correct.
Continuous Spectrum Citations
- Influence of Continuous Spectrum Light on Morphological Traits and Leaf Anatomy of Hazelnut Plantlets. Front Plant Sci . 2019 Oct 24;10:1318.
- Continuous-Spectrum Infrared Illuminator for Camera-PPG in Darkness. Sensors (Basel) . 2020 May 27;20(11):3044.
- From period to quasiperiod to chaos: A continuous spectrum of orbits of charged particles trapped in a dipole magnetic field. Chaos . 2020 Dec;30(12):123108.
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Angular Momentum: Definition, Formula, and Examples
Continue ReadingAngular Momentum
Angular momentum is referred to the property of any rotating object which is given by moment of inertia times angular velocity.
It is described as the property of a rotating body which is further given by the product of the moment of inertia and the angular velocity of the rotating object.
It is a vector quantity, which indicates angular momentum has both the magnitude, as well as the direction.
The angular momentum is a vector quantity and is represented by the symbol L→
It is represented in the SI units: Kg.m2.s-1
The dimensional formula for angular momentum is given by: [M][L]2[T]-1
Angular Momentum Formula
Angular momentum can be experienced by material in only two situations. They are given below:
• Point object: The object which accelerates around a fixed point. For instance, Earth revolves around the sun where the sun is considered to be the fixed point. Thus, the angular momentum is given by:
L→ = r×p→
Where,
L→ represents the angular velocity
r represents the radius [ that is the distance between the object (example; earth) and the fixed point(example; sun) ]
p→ represents the linear momentum.
• Extended object: The object, which is rotating about a fixed point or on its own axis. For example, Earth rotates on its axis. Here the angular momentum is given by:
L→ = I×ω→
Where,
L→ represents the angular momentum.
I represents the rotational inertia.
ω→ represents the angular velocity.
Angular Momentum Quantum Number
Angular momentum quantum number is similar to the Azimuthal quantum number as an angular quantum number also describes the shape and size of an atomic orbital. Its value generally ranges from 0 to 1.
Angular Momentum and Torque
Consider the point mass which is attached to a string, the string is further tied to a point, and now when we exert a torque on the point mass, it will thus start rotating around the center.
The particle having mass m will travel with a perpendicular velocity V which is the velocity that is perpendicular to the radius of the circle and r represents the distance of the particle for the center of its rotation.
The magnitude of L→
L = r.m.v sin ϕ
= r p⊥
= r.m.v⊥
= r⊥p
= r⊥mv
Φ represents the angle between r→ and p→
p⊥ and v⊥ are referred to as the components of p→ and we know that v→ is perpendicular to r→.
Note: In The equation L = r⊥mv the angular momentum of the body only varies when a net torque is applied to it. Therefore, when no torque is applied, then the perpendicular velocity of the body will thus depend upon the radius of the circle that is the distance from the center of mass of the given body to the center of the circle.
Thus, it can be said that;
1. For a shorter radius, the velocity will be high.
2. But, for a higher radius, the velocity will be low.
Right-Hand Rule
The direction of angular momentum is often given by the right-hand rule, which further states that;
Primarily, position your right hand such that the fingers lie in the direction of r.
Then curl the fingers around the palm in such a way that they start to point towards the direction of Linear momentum(p).
The extended thumb will provide us with the direction of angular momentum(L).
Examples of Angular Momentum
Ice-skater: An ice skater generally goes for a spin by keeping her hands and legs far apart from the center of the body. But when she wants more angular velocity to spin, then she keeps her hands and leg closer to her body. Therefore, her angular momentum is conserved, and thus she spins faster.
Gyroscope: A gyroscope commonly uses the principle of angular momentum to sustain its orientation. It uses a spinning wheel that has 3 degrees of freedom. When the wheel is rotated at a very high speed then it locks on to its orientation, and hence won’t deviate from its alignment. This is convenient in space applications where the attitude of a spacecraft is a vital factor that needs to be controlled.
Conservation of Angular Momentum
Angular momentum is referred to the rotational analog of linear momentum, it is represented by the symbol l, and the angular momentum of a particle in rotational motion is defined as follows:
l = r × p
This is a cross product of r which is the radius of the circle and is formed by the object in rotational motion, and p represents the linear momentum of the body. The magnitude of angular momentum is given by,
l = r p sinθ
Conservation of Angular Momentum Applications
The Law of conservation of angular momentum has several applications which further include; Aircraft engines, Electric generators, etc.
Difference Between Angular Momentum and Momentum
Momentum Angular Momentum Momentum or linear momentum is referred to as the mass in motion and is useful in measuring the quantity of motion of an object. Angular momentum is defined as the momentum of rotation and is considered to be the rotational analog of linear momentum. The SI unit for momentum is represented in kg m/s. The SI unit for momentum is represented in kg m^2/s. Momentum is defined as the product of the mass of an object and its velocity. Angular momentum is defined as the product of the Moment of inertia for mass and its angular velocity. Momentum is generally conserved when there are no external forces act. Angular momentum is generally conserved when no net torques are involved. Angular Momentum Citations
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Planck Quantum Theory: Definition, Properties, and Examples
Continue ReadingPlanck Quantum Theory
According to Planck’s quantum theory;
1. Different atoms and molecules produce or absorb energy in discrete quantities only. The smallest amount of energy that can be emitted or absorbed by an electron in the form of electromagnetic radiation is termed as quantum.
2. The energy of the radiation which is absorbed or emitted is directly proportional to the frequency of the electromagnetic radiation as given below.
The energy of radiation is represented in terms of frequency as follows;
E = h ν
Where,
E signifies the Energy of the radiation
h signifies Planck’s constant (6.626×10–34 J.s)
ν signifies the Frequency of radiation
Later in the year 1905, famous German physicist, Albert Einstein re-explained Planck’s theory to further describe the photoelectric effect. He believed that when some source of light is focused on certain materials, then they eject electrons from the surface of that material. Planck’s work led Einstein in determining that light occurs in discrete quanta of energy, or these quanta of energy is termed as photons. Planck was successful in explaining the phenomenon of black body radiation by assuming that absorption and emission of radiation arise from an oscillator that is the atoms in the wall of a black body.
This theory states that;
(a) The radiation energy emitted or absorbed are present in the form of small packets of energy (that is in discrete quantities and not in a continuous manner). Such packets are termed as quantum or photons.
E ∝ ν
E = hν (h = 6.6 x 10-34 Js)
(b) Energy of each photon is directly proportional to the frequency of radiation. Where ‘h’ represents the Planck’s constant. E represents the energy of a photon.
Planck Quantum Theory
As progress in the science field was happening, Maxwell’s idea about the wave nature of electromagnetic radiation helped to describe phenomena such as interference, diffraction, etc. Though he was unable to explain several other phenomena such as the photoelectric effect, that is ejection of electrons from the surface of a metal compound when electromagnetic radiation strikes it, line spectra of atoms (specifically hydrogen), black -body radiation.
Black Body Radiation
Solids, when heated, produce radiation of a wide range of wavelengths. For instance: when we heat a solid colour, then a change of colour is observed and this continues with a further increase in temperature. This colour change generally happens from a lower frequency region to a higher frequency region as the temperature rises. For instance, in several cases, the colour changes from red to blue. An ideal body that can emit or absorb radiation of all frequencies is termed as a black body.
The radiation emitted by such bodies is termed black body radiation. Thus, it can be said that the variation of frequency for black body radiation generally depends on the temperature. At a certain temperature, it was found that the intensity of radiation increases with an increase in the wavelength of radiation. This phenomenon was not explained by Maxwell’. Hence, Planck projected Planck’s quantum theory to explain this phenomenon.
Electromagnetic Radiation
Electromagnetic radiation is referred to as a form of energy that can propagate in a vacuum or any material medium and hence shows both wave-like and particle-like properties.
Radio waves, microwaves, infrared, visible light, UV-rays, X-rays, gamma rays are some examples of electromagnetic radiation.
Materials having low temperature generally emit radiowaves or microwaves (low-frequency waves) while objects having high temperature usually emit visible light or ultraviolet light.
A black body is referred to as an idealized object that absorbs all electromagnetic radiation that comes in contact with it. After absorption, it starts producing thermal radiation in the form of a continuous spectrum according to its temperature. The radiation emitted by a black body is termed as black body radiation.
What is Planck Quantum Theory?
Planck’s quantum theory describes the emission and absorption of radiation by electrons. Postulates of Planck’s quantum theory are given below;
1. Matter emits or absorbs radiation in the form of small packets or bundles.
2. These small bundles or packets of energy are termed as quantum.
3. The energy of the quantum absorbed or produced is directly proportional to the frequency of the radiation. So, the energy of the radiation is generally stated in terms of its frequency as follows-
A body can emit or absorb energy in whole-number multiples of a quantum given by nhv.
Where n represents a positive integer
The Energy can be absorbed or radiated as hv, 2hv, 3hv, 4hv……etc but it cannot emit or absorb radiation in the form of 1.5hv, 2.5hv…etc.
After Max Planck, a German physicist named Albert Einstein enhanced the theory and also explained the photoelectric effect.
Evidence in Support of Planck Quantum Theory
Many experiments were executed to examine Planck’s quantum theory. But, all experimental explanations supported and worked as solid evidence for quantum theory. It thus shows that the energy of an electron in the matter is always quantized. The emission spectrum of nitrogen gas thus supports Planck’s quantum theory of radiation.
Applications of Planck Quantum Theory
Planck’s quantum theory is considered to be an important theory of quantum mechanics. Some applications of Plank’s quantum theory includes;
Electrical Appliances
Medical Field
Quantum Computing
Lasers
Quantum Cryptography and many more.
Planck Quantum Theory Examples
Q1. A violet light has a wavelength of 380nm. Determine the energy for the violet light in joules.
Solution: To find the Frequency , the formula used is ,
c = λ×v
Where,
c represents the speed of light
λ represents the wavelength of violet light
v represents the frequency of light
Now,
v = 3×108 / 380 × 10-9 [ 1 nm = 10-9 m]
Hence,
v = 7.89×1014/s
To find the Energy , we know that E = h×ν
Where, h represents the planck’s constant
= (6.626×10−34)×(7.89×1014)
= 8.39 ×10−19 joule /photon
Planck Quantum Theory Citations
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Bohr Orbit: Definition, Properties, and Examples
Continue ReadingBohr Orbit Definition
The Bohr model proposed that the electrons present in atoms revolve around the nucleus in a fixed path termed as bohr orbits or energy shells.
In atomic physics, an atom is defined by the Bohr model as a small, positively charged nucleus that is surrounded by negatively charged particles called electrons.
Overview of the Bohr Model
Niels Bohr projected the Bohr Model of the Atom in the year 1915. The Bohr Model has some drawbacks but this model is vital to study because it describes most of the accepted features of atomic theory without the high-level math of the modern version.
The Bohr Model also describes the Rydberg formula for the spectral emission lines of atomic hydrogen. Bohr model of atom described the planetary model which states that the negatively charged electrons revolve around a positively charged nucleus like the planets orbit the sun. The gravitational force of the solar system is scientifically similar to the electrical ( or Coulomb ) force between the nucleus and electrons.
The Bohr model was the modification of the earlier cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and lastly the Rutherford model (1911).
The Rydberg formula for the spectral emission lines of atomic hydrogen was successfully explained by Bohr. Apart from this, the Bohr model also explained the structure of the Rydberg formula, he also justified its experimental results in terms of fundamental physical constants.
Bohr Model of Hydrogen
The simplest example used to explain the Bohr Model is the model of a hydrogen atom (Atomic number or Z= 1) or for a hydrogen-like ion (Z > 1), in which a negatively charged particle termed as electron revolve around a positively charged nucleus. Electromagnetic energy is either absorbed or emitted when an electron jumps from one orbit to another.
Methodically, the value of the atomic radius is as follows:
r(n)=n2×r(1)
Where,
• n signifies a positive integer
• r(1) signifies the value of the smallest allowed radius for the hydrogen atom also termed as Bohr’s radius.
Important Equations
The equation used to find the Radii of Bohr’s stationary orbits is;
rn = n2 (h2εo/πmZe2)
• n denotes integer
• rn denotes the radius of the nth orbit
• h denotes Planck’s constant
• ε0 signifies the Electric constant
• m signifies the mass of the electron
• Z signifies the Atomic number of the atom
• e signifies Elementary charge
The equation used to find the velocity of Electron in Bohr’s Stationary orbit is;
vn = (Ze2/2hεo)(1/n)
ε0, h, and e are the constants and for a hydrogen atom, Z or atomic number is 1 Hence, rn α (1/n)
Total Energy of Electron in Bohr’s Stationary Orbits is;
En = -(me4/8ε02h2)(Z2/n2)
En = -13.6(Z2/n2)eV
The negative sign indicates that the electron is bound to the nucleus. The energy therefore obtained is always a negative number.
Bohr Model for Heavier Atoms
Heavier atoms comprises of more protons in the nucleus as compared to a hydrogen atom( as atomic number = 1). So, more number of electrons were required to cancel out the positive charge of these protons. Bohr stated that each electron orbit or shell could only hold a fixed number of electrons. Once this energy level is filled, then additional electrons would jump to the next level. Therefore, the Bohr model for heavier atoms explained electron shells. This model also explained some of the atomic properties of heavier atoms.
Properties of Electrons under the Bohr Model
In 1913, Bohr proposed that electrons could only have certain standard motions:
1. Electrons (negatively charged particles) present in atoms orbit the nucleus.
2. The electrons can only revolve in a certain orbit, at a discrete distance from the nucleus. These orbits are linked with certain energies and are also termed as energy shells or energy levels.
3. Electrons can only absorb or emit energy by jumping from one orbit to another orbit.
Merits of Bohr Model
1. The Bohr model was the primary model to suggest the quantization of electron orbits in atoms. Hence, it specifies an early quantum theory that also gave a way to the development of modern quantum theory. It also presented the concept of a quantum number to explain the atomic states of an atom.
2. Bohr also described the stability of atoms.
3. He described the spectrum of hydrogen and he also calculated the size of an atom.
Limitations of Bohr Model
• The Bohr Model was unable to explain the fine structure and hyperfine structure in the spectral lines.
• The Bohr atomic model theory correctly described the structure of small-sized atoms for instance – hydrogen, but for larger atoms, poor spectral predictions are attained. Therefore, Bohr failed to explain the structure of large-sized atoms.
• The Zeeman effect (which states that the spectral line usually splits into several components in the presence of a magnetic field) could not be described by Bohr.
• The Stark effect(which further states that the spectral line generally splits into fine lines in the presence of an electric field) could not be explained by Bohr.
• Bohr model of the atom was unable to predict the relative intensities of several spectral lines.
The Bohr model explained the structure of hydrogen atom and other single-electron structures. Unfortunately, he failed to explain the spectra of more complex atoms. Furthermore, the Bohr model also failed to explain why some spectral lines are more intense as compared to other lines or why some spectral lines split into numerous other lines in the presence of a magnetic or electric field.
This phenomenon of splitting of spectral lines in presence of a magnetic field is termed as the Zeeman effect and the splitting of spectral lines in presence of an electric field is termed as the stark effect. In the following decades, several theories were proposed by different scientists such as Erwin Schrödinger stated that electrons can be assumed to behave like waves as well as particles.
This further means that it is not possible to know an electron’s location in space as well as its velocity at the same time, a concept that is described by Heisenberg.
Bohr Orbit Citations
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Electromagnetic Spectrum: Definition, Properties, and Examples
Continue ReadingElectromagnetic Spectrum Definition
In simple terms, the Electromagnetic spectrum can be defined as the range of all types of electromagnetic radiation and waves. All celestial bodies emit electromagnetic energy of different wavelengths. Mostly, electromagnetic waves tend to travel at speeds that is similar to the speed of light in a vacuum.
Light is a specific type of electromagnetic radiation that can be seen and detected by the human eye, but this energy generally occurs at a wide range of wavelengths. The spectrum of waves is further divided into sections based on their wavelength. The shortest waves are gamma rays, having wavelengths of 10-6 microns or less. The longest waves are radio waves, having wavelengths is of many kilometres.
Electromagnetic Waves in Electromagnetic Spectrum
The entire electromagnetic spectrum is given by the following;
Radio Waves
Microwaves
Infrared Radiation
Visible Light
Ultra-Violet Radiation
X-Rays
Gamma Rays
Radio: A radio fundamentally captures radio waves that are further transmitted by radio stations. Radio waves can also be produced by gases and stars in space. Radio waves are largely used for TV or mobile communication. Extremely low frequency (ELF) radio waves of about 1 kHz or kilohertz are used to communicate with submerged submarines.
The capability of radio waves to penetrate saltwater is linked to their wavelength that is the longer the wavelength, the farther radio waves can penetrate. Saltwater is a good conductor of electricity, hence radio waves are strongly absorbed by it, and thus very long wavelengths (such as radio waves have long wavelengths) are required to reach a submarine under the water surface.
Microwave: This type of radiation is commonly found in microwaves and thus helps in cooking. It is also used by astronomers to comprehend the structure of galaxies and stars in space. Microwaves are referred to as the highest-frequency electromagnetic waves that can be formed by currents in macroscopic circuits and devices.
Infrared: It is used extensively in night vision goggles. In space, infrared light is used to map interstellar dust. Infrared radiation is commonly produced by thermal motion and the vibration and rotation of atoms and molecules.
X-ray: X-rays are used in many instances. For instance, a doctor uses an x-ray machine to capture an image of our bone or teeth. Airport security personnel use X-rays to see through our bags. X-rays have harmful effects on living cells like those of ultraviolet radiation, and they can be more penetrating, thus affect the surface layers of cells.
Gamma-ray: It has an extensive application in the medical field. The universe is the biggest producer or generator of gamma rays. Soon after nuclear radioactivity was first noticed in the year 1896, it was found that at least three different types of radiation were being emitted. It was found that the most penetrating nuclear radiation was the gamma-ray (γ ray) and have an extremely high frequency.
Generally, at higher frequencies, γ rays are more penetrating and more destructive to living tissue. Gamma radiation produced from radioactive materials is also used in nuclear medicine.
Ultraviolet: The main source of ultraviolet radiation is the sun. Hot materials that are present in space also produce UV radiation. Ultraviolet is also formed by atomic and molecular motions and electronic transitions. The wavelengths of ultraviolet ranges from about 400 nm to about 10 nm.
Visible: Visible light can be detected by the naked eye. Stars, bulbs, etc. emit visible light. Visible light is the narrow section of the electromagnetic spectrum to which the human eye responds. Visible light is commonly formed by vibrations and rotations of atoms and molecules, and also by electronic transitions in atoms and molecules. The receivers or detectors of light largely utilize electronic transitions.
Spectroscopy
Spectroscopy is a method used to study the interaction of different electromagnetic waves with matter.
Significance of Electromagnetic Spectrum
The electromagnetic waves in these different bands have different features depending upon their production and interaction with matter. Maxwell’s equations projected the existence of a countless number of frequencies of electromagnetic waves, all moving with the speed of light.
Nevertheless, the key significance of the electromagnetic spectrum is that it can be used to categorize electromagnetic waves and also helps in arranging them according to different frequencies or wavelengths.
Practical Applications of Electromagnetic Waves
● The visible light portion of the electromagnetic spectrum helps us to see all the objects, as well as the colours.
● The X-rays discovered by Roentgen is quite useful in medicine in recognizing various ailments or deformities in bones.
● The high ultraviolet radiation usually has high energies used to ionize the atoms, hence causing many chemical reactions.
● The gamma rays discovered by Paul Villard are also useful for the ionization process.
Electromagnetic Radiation Equation
Electromagnetic radiation is generally expressed in terms of energy (or abbreviated as E), wavelength( or represented as λ), frequency.
Frequency is usually measured in cycles per second (Hertz or Hz).
Wavelength (λ) is commonly measured in metres.
Energy is measured in electron volt ( eV).
Each of these three quantities mentioned above are linked to each other in a specific scientific way.
f = c/λ
f = E/h
E = hc/λ
Where;
c represents the speed of light in a vacuum
h represents is Planck’s constant that is 6.62607015×10−34 J·s
Electromagnetic Spectrum Examples
Q1. What are the frequency and wavelength of an Electromagnetic wave of energy 5.83 x 10-19 J?
Answer: We know the Frequency(f) = E/h Where,
E represents the energy
h represents the planks constant that is 6.62×10−34 J·
So frequency is 8.80 x 1014 Hertz or Hz
We know that Wavelength ( or λ) = c/f Where, c represents the speed of light that is 3 x 108
f represents the frequency
So,
wavelength = 3 x 108 / 8.80 x 1014
= 0.3409 x 10-6 metres
Electromagnetic Spectrum Citations
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Emission Spectrum: Definition, Properties, and Examples
Continue ReadingEmission Spectrum
When electromagnetic radiations interact with atoms and molecules of matter, then the electrons present in these atoms may absorb energy and move to a higher energy state, losing their stability. To regain their stability, they then move from the higher energy state back to the lower energy state. These atoms and molecules produce radiations in several regions of the electromagnetic spectrum while jumping between different energy levels. This spectrum of radiation which is emitted or produced by electrons in the excited atoms or molecules is termed as the emission spectrum.
In simple words, The emission spectrum of a chemical element or compound is referred to the spectrum of frequencies of electromagnetic radiation produced or emitted by an atom or molecule making a transition from a high energy state to a lower energy state.
Atomic Spectra
• When a ray of white light falls on a prism, it generally experiences refraction twice. Primarily, when the light travels from the rarer medium (example; air) to a denser medium (example; glass) and secondly when the light from the denser medium (example; glass) to a rarer medium (example; air).
• Lastly, a band of colours, called spectrum is observed. On observing this spectrum more thoroughly, it was found that the colour having a smaller wavelength deviates the most.
• Hence, a spectrum of colours ranging from red to violet is seen where the colour red has the longest wavelength and thus suffers the least deviation. This type of spectrum is termed as a continuous spectrum.
• Though, the emission spectrum of atoms present in its gas phase, do not show a continuous spread of the wavelength from one colour to another. Instead, the emitted light contains a specific wavelength having dark spaces between them. Such type of spectra is further known as atomic spectra or line spectra.
Absorption Spectrum
An absorption spectrum is similar to a photographic negative of the emission spectrum. For detecting the absorption spectrum, electromagnetic radiations are bombarded on a sample that absorbs radiation of certain wavelengths. The wavelength of radiations thus absorbed by the matter will contribute to the missing wavelength by leaving dark spaces in between the bright continuous spectrum. Each element has its exclusive line emission spectrum. Spectroscopy refers to the study of the emission spectrum or absorption spectrum.
Hydrogen Emission Spectrum
• Electrons present in an atom or a molecule absorb energy and then moves from a lower energy level to a higher energy level, on the other hand, electrons emit radiations when they come back to their original states. This phenomenon also accounts for the emission spectrum termed as a hydrogen emission spectrum. The emission spectra of molecules are commonly used in the chemical analysis of elements.
• The hydrogen spectrum is a significant piece of evidence that further shows that the electronic structure of the atom is quantized. When an electric discharge is passed through a gaseous hydrogen molecule, it was found that the hydrogen atoms present in the molecule dissociate thus leading to the emission of electromagnetic radiation by the excited hydrogen atoms. The hydrogen emission spectrum generally comprises of radiations of distinct frequencies.
• When a hydrogen atom absorbs a photon then the energy of the photon causes the electron to undergo a transition to a higher energy level (for instance n = 2 n = 3). On the other hand, when a hydrogen atom produce or emit a photon, the electron thus undergoes a transition from a higher energy level to a lower energy state (for instance; n = 4 n = 3) During this transition that is from a higher energy level to a lower energy level, a transmission of light occurs. As the energy levels of the atom are quantized, the spectrum formed will contain wavelengths that will further reflect the differences in the energy levels.
Hydrogen Emission Spectrum Series
In the year 1885, based on his experimental explanations, Balmer suggested the formula for associating the wavenumber of the spectral lines and the energy shells involved. This formula is as follows:
ν¯ =109677 (1/22 – 1/n2)
Where, ν¯ signifies the wavenumber of electromagnetic radiation. This series of the hydrogen emission spectrum mentioned above is termed as the Balmer series.
It is easy to calculate the spectral lines by using the Rydberg formula;
1/λ = RZ2 [(1/nf2) – (1/ni2)]
Where,
• h signifies Planck’s constant
• c signifies the speed of light
• Z signifies the atomic number
• n1 and n2 are whole numbers representing the energy levels such that n1 < n2.
• The value of the Rydberg constant, RH is equal to 1.0967 x 107 m-1
The Balmer series is the part of the hydrogen emission spectrum which is further accountable for the excitation of an electron from the second energy shell to any other shell. Likewise, other transitions have their series names.
For instance; Paschen series, Lyman series etc. The spectral lines observed are because of the jumping of electrons between different energy levels in the atom.
The spectral series are significant to study because in astronomy it is used for detecting the presence of hydrogen.
Emission Spectrum vs Absorption Spectrum
Emission Spectra Absorption Spectra This type of spectrum is produced when atoms release or emit energy This type of spectrum is produced when atoms absorb energy Emission spectrum consists of coloured lines Absorption spectrum consists of dark lines or gaps It is very helpful in analzing the composition of a certain matter This can be used often to figure out the capability of objects to retain heat and its absorption level Emission Spectrum Citations
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Bohr Model of Hydrogen Atom: Definition and...
Continue ReadingBohr Model of Hydrogen Atom Equation
Bohr Model of the hydrogen atom initially projected the planetary model, but later an assumption regarding the electrons was made. The assumption made was the quantization of the structure of atoms. Bohr’s projected that electrons revolved around the nucleus in specific paths termed as orbits or shells with a fixed radius.
Scientifically, the value of the atomic radius is given by the equation as follows:
r(n)=n2×r(1)
Where,
• n represents a positive integer
• r(1) represents the smallest allowed radius for the hydrogen atom also called as Bohr’s radius
Planetary Model of the Atom
Quantum mechanics arose in the mid-1920s. Neil Bohr, one of the founders of quantum mechanics, was involved in the much-debated topic of that time which is the structure of an atom. Several atomic models, including the theory proposed by J.J Thompson and the finding of a nucleus by Ernest Rutherford, had arisen over time. But Neil Bohr proposed the planetary model, which stated that electrons revolve around a positively charged nucleus just like the planets orbit around the sun.
Bohr Model of Hydrogen Atom
Bohr’s model of the hydrogen atom initially started from the planetary model, but he further added one assumption concerning the electrons. Bohr proposed that the electrons present in an atom could only orbit the nucleus in definite orbits or shells with a fixed radius.
By considering the electrons in circular, quantized orbits revolving around the positively charged nucleus, Bohr also determined the energy of an electron.
Absorption and Emission
The energy level diagram shown below displays transitions for the Balmer series, it has the n=2 energy level as the ground state.
Bohr was successful in describing the processes of absorption and emission of electrons. According to Bohr’s model, an electron generally absorbs energy in the form of photons to get excited to a higher state. This higher energy level is also known as the excited state. After reaching the higher energy level the excited electron would be in a less stable state, and consequently, the electron would quickly emit a photon and will be back to its lower, more stable energy state.
The energy of the emitted photon is thus equal to the difference in two energy levels for a definite transition.
The energy can be determined by using the equation given below;
hν = z2me4/8h2ε02 [(1/n12) – (1/n22)]
= -13.6z2 [(1/n12) – (1/n22)]eV
Bohr Model of Hydrogen Atom: Some Important Equations
The equation to find the Radii of Bohr’s stationary orbits is as follows;
rn = n2(h2εo/πmZe2)
• n represents integer
• rn represents the radius of the nth orbit
• h represents Planck’s constant
• εo represents the Electric constant
• m represents the mass of the electron
• Z represents the Atomic number of the atom
• e represents Elementary charge
The equation to find the velocity of Electron in Bohr’s Stationary is;
vn = (Ze2/2hεo) (1/n)
Since εo, h, and e are the constants and for a hydrogen atom, Z or atomic number is equal to 1
Hence,
rn α (1/n)
Total Energy of Electron in Bohr’s Stationary Orbits is given by;
En = -(me4/8εo2h2)(Z2/n2) or
En = -13.6 (Z2/n2) eV
The negative sign signifies that the electron is bound to the nucleus. The energy thus obtained is always a negative number.
However, these equations were derived by assuming that the electron revolves around the nucleus in a circular path, further experiments directed by Arnold Sommerfeld stated that these equations are applicable even for elliptical orbits.
Energy Levels
The minimum energy required to release an electron from the ground state of an atom is equal to 13.6 eV. This energy is termed as the ‘Ionization Energy’ of the hydrogen atom.
E1 = -13.6 eV
A hydrogen atom is generally present in the ‘Ground State’ at room temperature. The atom might take energy from various processes such as electron collision and thus gains enough energy to move the electron to higher energy states or orbits. This is termed as the ‘excited’ state of the atom. Hence, the energy that is required by the atom to excite an electron is as follows;
E2 – E1 = -3.40 eV – (-13.6) eV = 10.2 eV
Correspondingly, the energy required to excite the electron to its second excited state is as follows:
E3 – E1 = -1.51 eV – (-13.6) eV = 12.09 eV
Bohr model of the hydrogen atom was the first atomic model to effectively describe the radiation spectra of atomic hydrogen. Niel Bohr presented the atomic Hydrogen model in the year 1913. Bohr’s model of atom holds a distinct place in the past as it gave rise to quantum mechanics by proposing the quantum theory.
Limitations of the Bohr Model of Hydrogen Atom
• Bohr’s model explained the structure of simple atoms such as hydrogen but failed to explain the structure for complex atoms.
• Bohr was unable to explain that why some spectral lines are more intense than others.
• Heisenberg’s uncertainty principle opposes Bohr’s idea of electrons. According to Bohr’s model of the atom, an electron present in an atom is positioned at a fixed distance from the nucleus and is revolving with a definite velocity around the positively charged nucleus.
But Heisenberg’s uncertainty principle states that it is nearly impossible to determine the exact position and velocity (or momentum) of the electron at the same time.
The Bohr model helped in explaining the structure of hydrogen atom and other single-electron structures. Unfortunately, he was unable to explain the spectra of more complex atoms. Moreover, the Bohr model failed to explain why some lines are more intense as compared to other lines or why some spectral lines split into several lines in the presence of a magnetic field. This phenomenon of splitting of spectral lines in presence of a magnetic field is termed as Zeeman effect.
In the following decades, the theories proposed by different scientists such as Erwin Schrödinger presented that electrons can be assumed to behave like waves as well as particles. This further means that it is not possible to know an electron’s location in space and its velocity at the same time, a concept that is stated in Heisenberg’s uncertainty principle.
Bohr Model of Hydrogen Atom Citations
- Why has the bohr-sommerfeld model of the atom been ignoredby general chemistry textbooks? Acta Chim Slov . 2011 Dec;58(4):876-83.
- Realization of localized Bohr-like wave packets. Phys Rev Lett . 2008 Jun 20;100(24):243004.
- Bohr’s 1913 molecular model revisited. Proc Natl Acad Sci U S A. 2005 Aug 23; 102(34): 11985–11988.
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Limitations of Bohr Model: Definition, Properties, and...
Continue ReadingBohr Model
Bohr model of the atom was proposed by Neil Bohr in the year 1915. It was an extended modification of Rutherford’s model of an atom. Rutherford made the first discovery by presenting the model of an atom, in which he described that a nucleus (a positively charged particle) is surrounded by an electron which are negatively charged particles. Though this model has some discrepancies or drawbacks, Bohr tried to resolve them in his model.
Bohr with his enhanced version of atomic structure proposed that electrons always move in a fixed path called orbits or energy shells and he also explained that each orbit (or energy shell) possessed a fixed energy level.
Rutherford primarily described the nucleus of an atom and Bohr reformed that model into electrons and their energy levels.
Bohr Model of an Atom
Bohr model atom comprises of a small nucleus (positively charged) surrounded by negatively charged particles termed as electrons which revolve around the nucleus in fixed energy shell called orbits.
Bohr stated that an electron situated away from the nucleus has more energy, as compared to electrons close to the nucleus.
Postulates of Bohr Model of an Atom
• In an atom, electrons (negatively charged particles) rotate around the positively charged nucleus in a fixed path called orbits or energy shells.
• Each orbit or energy shell has fixed energy.
• The energy levels of the shell are characterized by a simple whole number (that is n=1, 2, 3…) often designated as the quantum number. The orbits n=1, 2, 3, 4… are also known as K, L, M, N…. shells, and when an electron is present at the lowest energy level, it is said to be present in the ground state.
• Electrons present in an atom gains energy when it moves from a lower energy level to a higher energy level, however, if the electron jumps from a higher energy level to lower energy, then the energy is emitted.
• The energy absorbed or emitted is always equal to the difference between the energies of the two given energy levels (that is E1 and E2) and is determined by Plank’s equation. The equation for the same is given below;
ΔE = E2-E1 = hv
Where,
ΔE represents the energy that is absorbed or emitted
h represents Plank’s constant
v represents the frequency of electromagnetic radiation emitted or absorbed
Limitations of Bohr Model
• Bohr’s theory of the atomic model was quite effective in explaining the stability of the atom and the line spectrum of a hydrogen atom.
• Orbits were presumed to be circular but Sommerfield further stated that these orbits are elliptical.
• The intensity of spectral lies could not be clarified by Bohr.
• The nucleus was told to be stationary or inactive but it was later revealed that the nucleus (positively charged particle) revolves around its own axis.
• Bohr model of the atom was unable to explain the Zeeman effect (that is splitting up of spectral lines in the magnetic field) and Stark effect (that is splitting up in electric field)
Significant Limitations of Bohr Atomic Model
• Bohr was not able to explain the shapes of the molecule due to the directional bonding between atoms. This model has a very incomplete approach in terms of the size of atoms. The Bohr atomic model did not make precise predictions for large-sized atoms but it did provide adequate information for smaller atoms like hydrogen.
• Bohr was unable to explain the line spectra of atoms encompassing of more than one electron thus called as multi-electron atoms. According to Bohr’s model of the atom, one and only one spectral line can be created from an electron between any two energy levels. But by using powerful spectroscopy, it was further observed that certain single lines split into a number of very closely related lines. The existence of such a line could not be explained by Bohr.
• Bohr’s theory failed to explain the effect of the magnetic field on the spectra of atoms or ions. It does not explain the Zeeman Effect that is defined as the splitting of the spectral line into numerous other components in the presence of a magnetic field.
• Bohr’s theory failed to explain the effect of an electric field also termed as the Stark effect on the spectra of atoms. Stark Effect is defined as the splitting of the spectral line into a number of closely related lines in the presence of an electric field.
• The Bohr model violates the Heisenberg Uncertainty Principle because the Bohr Model considers electrons to have both a known radius as well as an orbit, which is not possible according to the Heisenberg principle. Bohr described that an electron in an atom revolves around a nucleus with explicit velocity, which means that it is associated with a fixed value of momentum. This further contradicted the Heisenberg’s Uncertainty Principle.
Thus, we find that Bohr’s model was partially successful. It did describe some of the experimental outcomes but was unable to explain the other features of the atom. Hence, the Bohr model of the atom was soon abandoned in the light of modern ideas relating to the wave characteristics of matter.
Refinements and Improvements to the Bohr Model
The most significant improvement in the Bohr model was done by Sommerfeld or the Bohr-Sommerfeld model. In this model, it was discovered that electrons travel in elliptical orbits around the nucleus rather than in circular orbits. The Sommerfeld model was also able to explain atomic spectral effects, such as the Stark effect. Though, the model failed to explain the magnetic quantum number. Eventually, the Bohr model and models based upon it were substituted by Pauli’s model which was based on quantum mechanics.
Limitations of Bohr Model Citations
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Photoelectric Effect: Definition, Properties, and Examples
Continue ReadingPhotoelectric Effect Definition
The photoelectric effect is referred to as a phenomenon in which electrons are ejected from the surface of a metal when light is incident on it. The electrons ejected are termed as photoelectrons. The emission of photoelectrons and the kinetic energy of the ejected photoelectrons is generally dependent on the frequency of the light that falls on the metal’s surface. Photoemission is referred to the process through which photoelectrons are ejected from the surface of the metal.
The photoelectric effect occurs because the electrons present at the surface of the metal tend to absorb energy when light that is incident on the surface of metal carries enough energy to overcome the attractive forces that usually bind the electrons to the atomic nuclei of the metals.
Photoelectric Effect Equation
According to Albert Einstein, the photoelectric effect is explained as follows:
Thus,
hν = W + E
Where
• h represents Planck’s constant.
• ν represents the frequency of the incident photon.
• W represents a work function.
• E represents the maximum kinetic energy of ejected electrons: 1/2 mv².
History of Photoelectric Effect
The photoelectric effect was initially observed by Wilhelm Ludwig Franz Hallwachs in the year 1887 and the experimental confirmation was done by the scientist Heinrich Rudolf Hertz. They detected that when electromagnetic radiation is incident on the surface of the metal at a higher threshold frequency, then the radiation is absorbed and the electrons are thus emitted.
Einstein’s Contributions towards the Photoelectric Effect
After constant research in this field, the description for the photoelectric effect was effectively explained by Albert Einstein. Einstein gave the equation as follows;
E = hν
Where;
E represents the Energy of a photon ( joules)
h represents planks constant (that is 6.626 × 10-34 J.s)
ν represents the frequency of photon in Hz or hertz
The Concept of Photons
The phenomena of the photoelectric effect cannot be described by considering light as a wave. Though, this effect can be described by the particle nature of light, which defines that light can be imagined as a stream of particles of electromagnetic energy. These ‘particles of light are thus termed as photons. The energy held by a photon is given below;
E = h𝜈 = hc/λ
Where,
• E represents the energy of the photon
• h represents Planck’s constant
• 𝜈 represents the frequency of the light
• c represents the speed of light (in a vacuum)
• λ represents the wavelength of the light
Therefore, it can be said that different frequencies of light generally carry photons of varying energies. For instance, the frequency of blue light is greater as compared to that of red light. Thus, the energy that is held by a photon of blue light will be greater as compared to the energy held by a photon of red light.
Properties of the Photon
• A photon is not reflected in a magnetic and electric field and it does not have any mass or charge.
• The momentum and energy of the photons are as follows;
E = pc
Where;
P represents the magnitude of the momentum
c represents the speed of light
Threshold Energy for the Photoelectric Effect
Threshold energy (represented by the symbol Φ)is referred to as the minimum amount of energy that is required to remove an electron from the metal. For a photon to hold energy equal to the threshold energy, then its frequency should be equal to the threshold frequency. The threshold frequency is expressed by the symbol 𝜈th and the linked wavelength ( also termed as the threshold wavelength) is expressed by the symbol λth. This can be represented (relation between threshold frequency and threshold wavelength) is as follows;
Φ = h𝜈th = hc/λth
The relationship between the energy of the photon and the kinetic energy of the emitted photoelectron is written below;
Ephoton = Φ + Eelectron
⇒ h𝜈 = h𝜈th + ½mev2
Where,
• Ephoton represents the energy of the incident photon, that is always equal to h𝜈
• Φ represents the threshold energy of the metal surface, which is always equal to h𝜈th
• Eelectron represents the kinetic energy of the photoelectron, which is always equal to ½mev2 (that is me = mass of electron = 9.1 x 10-31 kg).
If the energy of the photon is less than the threshold energy, then there will be no emission or production of photoelectrons. Therefore, the photoelectric effect will not occur if the energy of photon
th). When the frequency of the photon is equal to the threshold frequency that is 𝜈 = 𝜈th, then there will be an emission or release of photoelectrons, though their kinetic energy will be zero.
Condition Required for Photoelectric Effect
Threshold Frequency (γth) It is defined as the minimum frequency of the incident radiation that will create a photoelectric effect (that is referred to as expulsion of photoelectrons from a metal surface) is termed as the threshold frequency.
If γ represents the frequency of incident photon and γth represents threshold frequency, then;
• If γ < γTh, then this represents that no ejection of photoelectron will occur and, hence, no photoelectric effect.
• If γ = γTh, then this represents that photoelectrons are just ejected from the surface, yet the kinetic energy of the electron is equal to zero
• If γ > γTh, then this represents that the photoelectrons are ejected from the metal surface. Photoelectrons ejected have kinetic energy.
Threshold Wavelength (γTh)
γTh = c/γTh
Where, γTh represents the threshold wavelength or wavelength of the incident photon.
γTh represents threshold frequency
• If λ < γTh, then the photoelectric effect will occur and electron ejected will also have kinetic energy.
• If λ = γTh, then just the photoelectric effect will occur but the kinetic energy of the photoelectron that is ejected will be equal to zero.
• If λ > γTh, there no photoelectric effect will occur.
Applications of Photoelectric Effect
• It is used to produce or generate electricity in Solar Panels. These panels comprises of metal combinations that allow them to generate electricity from a varied range of wavelengths.
• Lighting sensors for example the ones which are used in smartphones enable automatic modification of screen brightness according to the lighting. This is because the amount of current that is produced through the photoelectric effect is usually dependent on the intensity of light that hits the sensor.
• Digital cameras can spot and thus record light because they also have photoelectric sensors that respond to diverse colors of light.
Photoelectric Effect Citations
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Quantum Number: Definition, Properties, and Examples
Continue ReadingQuantum Number Definition
Quantum numbers are often used to define the trajectory and the movement of an electron in an atom.
Quantum numbers are defined as the set of numbers that are used to determine the position and energy of the electron in an atom.
Types of Quantum Number
There are basically four quantum numbers;
i. Principal Quantum Number
ii. Azimuthal Quantum Number or Orbital angular momentum quantum number
iii. Magnetic Quantum Number
iv. Spin Quantum Number
Number Symbol Possible Value Principal Quantum Number n 1,2,3,4,… Azimuthal Quantum Number l 0,1,2,3,….(n-1) Magnetic Quantum Number m1 -l,….,-1,0,1,…l Spin Quantum Number ms +1/2,-1/2 i. Principal Quantum Number
• Principal quantum numbers are represented by the symbol ‘n’.The Principal Quantum Number denotes the principal energy level or shell in which an electron revolves around the positively charged nucleus.
• The principal quantum number are described in whole numbers with a value that is equal to one or greater than one (n = 1,2,3,4,5…..) The value of n=1 signifies the innermost electron shell of an atom, which further corresponds to the lowest energy state (or also known as the ground state) of an electron.
• Thus, it can be observed here that a principal quantum number (n) cannot be zero nor it can have a negative value.
• When a given electron absorbs energy, then it jumps from one principle shell to a higher shell, thus causing an increase in the value of n. Correspondingly, when electrons emit or produce energy, then they rapidly jump back into lower shells thus causing a decrease in value of n.
• The principal quantum number helps us in determining the energy shell of an electron. It was first considered to differentiate between different energy levels in the Bohr model of the atom but remains valid to the modern atomic orbital theory.
The energies of the numerous principal shells will follow the sequence as given below;
K < L < M < N < ….
1 < 2 < 3 < 4 < …..
ii. Azimuthal Quantum Number
• The azimuthal (or orbital angular momentum) quantum number determines the shape of a given orbital. It is represented by the symbol ‘l’ and its value is always equal to the total number of angular nodes present in the orbital.
• A value of the azimuthal quantum number designates an s, p, d, or f subshell which differ in shape. This value of l or Azimuthal Quantum number depends on the value of the principal quantum number.
• For instance, if n =3, the azimuthal quantum number or l can take the following values which are– 0,1, and 2.
• When l = 0, the subsequent subshell is an ‘s’ subshell. Likewise, when l =1 and l = 2, the resultant subshells are ‘p’ and ‘d’ subshells. Consequently, when n = 3, the three subshells that an atom can have are 3s, 3p, and 3d.
• Another example for the same includes when n = 5, the possible values of l or azimuthal quantum number are 0, 1, 2, 3, and 4. If l = 3, then this represents that there are a total of three angular nodes present in the atom. Angular momentum quantum number can have a set of positive values ranging from zero to (n − 1).
For the 1st Shell or K, n =1, thus the value of l will be 0
For the 2nd Shell or L, n = 2, thus the value of l will be 0 and 1
For the 3rd Shell or M, n = 3, thus the value of l will be 0, 1 and 2
For the 4th shell or N, n = 4, thus the value of l will be 0, 1, 2 and 3
iii. Magnetic Quantum Number
The magnetic quantum number determines the total number of orbitals present in a subshell and the orientation of these orbitals. It is represented by the symbol ‘m1’.
The value of the magnetic quantum number depends on the value of the azimuthal quantum number.
For a known value of l, the value of ml ranges from -l to +l.
For instance, if n = 3 and l = 2 in an atom, then the possible values magnetic quantum number can have are – -2, -1, 0, +1,and +2.
iv. Electron Spin Quantum Number
• The electron spin quantum number does no depend on the values of n, l, and ml. The electron spin quantum number helps in determining the direction in which the electron is spinning, and is represented by the symbol ms.
• The electron spin quantum number can have two values which are +½ and -½.
• The positive value of ms indicates an upward spin on the electron which is also termed as ‘spin up’ and is represented by the symbol ↑. The negative value of ms indicates downward spin, or it is also termed as ‘spin down’, which is represented by the symbol ↓.
• The value of ms can be summarised to ±½. and an orbital of an atom cannot hold more than two electrons.
Quantum numbers Meaning and Possible Values of quantum numbers Principal quantum number or n Electron shell, n can be greater than or equal to1 Azimuthal quantum number or l Subshells (s=0, p=1, etc.) , For a given value of n it can have values ranging from 0 to (n-1) Magnetic quantum number or m1 Total number and orientation of orbitals, l≥m1≥-l Electron spin quantum number or ms Represents the direction of electron spin, ms = ±½ Note: Hund’s rules states that two electrons of the same atom cannot have exactly the same set of quantum numbers.
Quantum Number Examples
Q1. What are the Possible ml values for l = 3?
The value of the magnetic quantum number commonly ranges from -1 to 1,
Thus, the possible values of ml or magnetic quantum number when l = 3 are: -3, -2, -1, 0, 1, 2, and 3.
Q2. An electron is present in its 2p orbitals. What are the possible values of n, l, and ml for this electron?
For the 2p orbital,
• Principal quantum number (n) = 2
• Azimuthal quantum number (l) = 1
• Magnetic quantum number (ml) = – 1 , 0 ,+ 1
Quantum Number Citations
- Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules. J Chem Phys . 2013 Nov 14;139(18):184101.
- Sorting Photons by Radial Quantum Number. Phys Rev Lett . 2017 Dec 29;119(26):263602.
- The splitting of atomic orbitals with a common principal quantum number revisited: np vs. ns. J Chem Phys . 2012 Apr 14;136(14):144112.
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