The threshold frequency for a certain metal is 3.3 × 10¹⁴ Hz. If the light of frequency 8.2 × 10¹⁴ Hz is incident on the metal, predict the cutoff voltage for the photoelectric emission.

Photoelectric equation

eV₀ = hv - ϕ_{0 ………………} equation(1)

Where e = Charge on an electron = 1.6 × 10^-19 C

V₀ = Stopping Potential

h = plank’s constant

v = frequency of photon

ϕ₀ = Work function of the metal

Threshold frequency is the minimum frequency at which photoemission starts taking place from a metal surface. It is represented by v_0.

At threshold frequency, stopping potential is zero and energy of the emitted electron is also zero. Energy provided by the incident photon is just sufficient to eject out electrons from the metal surface.

ϕ₀ = hv₀ ....................equ.02

V₀ = Threshold frequency

Putting value of ϕ₀ from equ.02 to equ.01

eV₀ = hv – hv₀

∴ V₀ = h (v-v₀)/ e = 6.63 × 10^-34 × (8.2-3.3) × 10¹⁴/1.6 × 10^-19

= 2.03 V

For photo emission cut of potential is equal to 2.03 V