Question

The work function of a metal is 2.5 × 10⁻¹⁹ J. (a) Find the threshold frequency for photoelectric emission. (b) If the metal is exposed to a light beam of frequency 6.0 × 10¹⁴ Hz, what will be the stopping potential?

(Use h = 6.63 × 10^-34J-s = 4.14 × 10^-15 eV-s, c = 3 × 10⁸ m/s and me = 9.1 × 10^-31kg)

Answer 1

Given :-

Work function of a metal, W₀ = 2.5 × 10⁻¹⁹ J

Frequency of light beam, v = 6.0 × 10¹⁴ Hz

(a) Work function of a metal,

W₀ = hv₀,

where h = Planck's constant

v₀ = threshold frequency

`therefore "v"_0 = W_0/h`

`⇒ v_0 = (2.5 xx 10^-19)/(6.63 xx 10^-34)`

`= 3.77 xx 10^14  "Hz"`

`= 3.8 xx 10^14  "Hz"`

(b) Einstein's photoelectric equation :-

`eV_0 = hv - W_0`,

where

v = frequency of light

V_0 = Stopping potential

e = charge on electron

`therefore V_0 = (hv - W_0)/e`

`= (6.63 xx 10^-34 xx 6 xx 10^14 - 2.5 xx 10^-19)/(1.6 xx 10^-19)`

`= (3.97 xx 10^-19 - 2.5 xx 10^-19)/(1.6 xx 10^-19) = 0.91 V`