Light of frequency 7.21 × 10¹⁴ Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 10⁵ m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?

Frequency of the incident photon, v =488 nm = 488 x 10^-9 m

Maximum speed of the electrons, v = 6.0 x 10⁵ m/s

Planck’s constant, h = 6.626 x 10^-34 Js

Mass of an electron, m = 9.1 x 10^-31 kg

For threshold frequency vo, the relation for kinetic energy is written as:

1/2 (mv² )=h(v-v₀ )

v₀ = v -mv² /2h

= (7.21 x 10¹⁴ ) – (9.1 x 10^-31) x (6.0 x 10⁵)² /2 x ( 6.626 x 10^-34 )

= (7.21 x 10¹⁴ ) -2.472 x 10¹⁴

= 4.738 x  10¹⁴ Hz

Therefore, the threshold frequency for the photoemission of electrons is 4.738 x 10¹⁴ Hz.