Threshold Frequency: Definition, Equation, and Examples

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Threshold Frequency Definition

The threshold frequency is defined as the minimum frequency of the incident radiation below which photoelectric emission or emission of electrons is not possible.

The threshold frequency refers to the frequency of light that will cause an electron to dislodge emit from the surface of the metal.

If γ signifies the frequency of incident photon and γth signifies threshold frequency, then;

• If γ < γTh, then this denotes that no ejection of photoelectron will occur.

• If γ = γTh, then this denotes that photoelectrons are just ejected from the surface of the metal, however, the kinetic energy of the electron is equal to zero.

• If γ > γTh, then this denotes that the photoelectrons are ejected from the metal surface. Photoelectrons ejected have some kinetic energy.

These trends are thus termed as the photoelectric effect.

Kinetic energy (K.E) is equal to half times the mass (or abbreviated as m) multiplied by the square of the velocity (or abbreviated as v) of the electrons as shown below;

K.E = 1/2 (mv2)

Photoelectric Effect

The photoelectric effect is referred to a phenomenon in which electrons are expelled or ejected from the surface of a metal when light is incident on it. Electrons thus emitted are also termed as photoelectrons.

Therefore, the threshold frequency is referred to as the frequency of the light which carries sufficient energy to extricate an electron from an atom.

According to Albert Einstein, the photoelectric effect is described as follows:


hν = W + E


• h signifies Planck’s constant.

• ν signifies the frequency of the incident photon.

• W signifies a work function.

• E signifies the maximum kinetic energy of ejected electrons: 1/2 mv².

The Work Function

The work function of a metal is referred to as the minimum amount of energy which is required to start the emission of electrons from the surface of the metal. The work function is expressed in electron volts. One electron volt is referred to as the energy required to move an electron across a potential difference of one volt. Different metals have characteristic work functions, and also distinctive threshold frequencies.

For instance, aluminum has a work function equal to 4.08 eV, however, potassium has a work function equal to 2.3 eV.

1eV = 1.6 x 10-19 Joule


A photon can be defined as a quantum of light that has zero rest mass and moves at the speed of light in the vacuum. The phenomena of the photoelectric effect cannot be defined by considering light as a wave. Though, this effect can be described by considering the particle nature of light, which further states that light can be imagined as a stream of particles of electromagnetic energy. Hence, these particles of light are termed as photons.

The energy held by a photon is as follows;

E = h𝜈 = hc/λ


• E signifies the energy of the photon

• h signifies Planck’s constant

• 𝜈 signifies the frequency of the light

• c signifies the speed of light (in a vacuum)

λ signifies the wavelength of the light

Work Function and Threshold Frequency Formula

The theory of the photoelectric effect was proposed by Einstein by using Max Planck’s theory of light energy. It was thus considered that each packet of light energy (or commonly called as photons) carried energy equal to hv where h represents a proportionality constant known as the Planck constant and v represents the frequency of the electromagnetic waves of light.

Kmax represents the maximum amount of kinetic energy carried by the atoms before leaving their atomic bonding.

To describe the threshold frequency the equation for the photoelectric effect can be written as follows:

Kmax = hv-W


W represents the work function of the metal. It is defined as the minimum energy that needs to be supplied to the metal body for the discharge of photoelectrons.

Now W can be written as follows:

W = hvo


vo represents the photoelectric threshold frequency of the electromagnetic radiation.

Threshold Frequency Applications

The concepts of threshold energy in photoelectric effect and threshold frequency find their application in several devices and processes. Some of which are as follows;

• Photoelectron Spectroscopy: Photoelectron spectroscopy measurements are often done in a high vacuum environment to avert the electrons from being dispersed by gas molecules that are present in the air. In this process, we use monochromatic X-rays or UV rays of known frequency and kinetic energy (K.E) to determine experimentally the composition of given area samples.

• Night Vision Devices: When Photons strike alkali metal or semiconductor material (such as gallium arsenide) in an image intensifier tube, then this causes the expulsion of photoelectrons because of the phenomena known as the photoelectric effect. This is further accelerated by an electrostatic field where electrons strike a phosphor-coated screen hence converting electrons back into photons. Signals are thus produced and intensified due to the acceleration of electrons. This concept which is mentioned here is used in night vision devices.

• Image Sensors: Television in the early days contained video camera tubes that made use of the photoelectric effect to convert an electronic signal into an optical image. Though, presently, the mechanism of television working has been reformed.

The concept of photoelectric emission, work function, and photoelectric threshold frequency are essential to understand quantum physical sciences. This is also required for constructing various devices and to study various other phenomena.

Threshold Frequency Examples

Q. Calculate the threshold frequency for a metal with a work function of 5 electron volt or eV?

Solution: The equation for work function is given as-

W = hvo

vo = W/h

Where h represents Planck’s constant

vo represents the threshold frequency of metal

Converting 5eV into Joules as we know

1eV = 1.6 x 10-19 Joule

So, 5 eV = 5 x 1.6 x 10-19 Joule

vo = (5 x 1.6 x 10-19) / (6.63 x 10-34)


vo = 1.20 x 1015 Hertz or Hz

Threshold Frequency Citations


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