For photoelectric emission, the threshold frequency is the

1. Analyze the question You are asked to define the threshold frequency in the photoelectric effect.

2. Explain the concept When light shines on a metal surface, electrons are emitted only if each photon carries enough energy to overcome the metal's work function (φ), which is the minimum energy needed to free an electron from the surface.

Photon energy is E = hf, where h is Planck's constant and f is the frequency of the light.

• If hf < φ, no electrons are emitted, no matter how bright the light is.
• If hf ≥ φ, electrons are emitted.

The threshold frequency (f₀) is the frequency at which the photon energy is exactly equal to the work function:

hf₀ = φ, so f₀ = φ/h

Einstein's photoelectric equation is hf = φ + KE(max), which can be written as hf = hf₀ + ½mv²(max).

3. Go through the options

• A. Maximum frequency: Wrong. Any frequency above f₀ also ejects electrons, so there is no maximum.
• B. Minimum frequency required to eject electrons: Correct. Below f₀ there is no emission, and f₀ is the lowest frequency that works.
• C. Frequency giving the greatest number of electrons: Wrong. The number of electrons depends on the intensity of the light, not its frequency.
• D. Frequency giving the greatest kinetic energy: Wrong. The kinetic energy increases as the frequency increases, so there is no single frequency that gives the "greatest" energy.

4. Answer The threshold frequency is the minimum frequency of incident radiation required to eject electrons from the metal surface.

5. Exam tip Remember: frequency decides the energy of each electron, and intensity decides how many electrons. The word "threshold" means a "doorway" or minimum level. Whenever you see "threshold", think "minimum".