Ultraviolet light of wavelength 2271 Å from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. If the stopping potential is –1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (∼10⁵ W m^–2) red light of wavelength 6328 Å produced by a He-Ne laser?

Given:

Wavelength of light, λ = 2271 Å = 2271 × 10^-10m

Power of mercury source, E = 100 Js^-1

Stopping potential, V_s = -1.3 V

Let frequency of light = v

Work function, Φ₀ is given by,

Φ₀ = hv-eV_s

Φ₀ =

Where,

h = Planck’s constant = 6.6 × 10^-34Js

c = speed of light = 3 × 10⁸m

λ = wavelength of light

e = charge on each electron = 1.6 × 10^-19C

Φ₀ =

Φ₀ = 6.64 × 10^-19J

Φ₀ = (6.64/1.6) × 10^-19 eV = 4.15 eV

Let v₀ be the threshold frequency of the metal,

Φ₀ = hv₀

v_{0 =} Φ₀/h

→ v₀ = 6.6 × 10^-19/ 6.6 × 10^-34

→ v₀ = 1.00. × 10^-15 s^-1

Wavelength of red light, λ’ = 6323 × 10^-10m

Frequency of red light can be given as,

v' = c/λ’

v’ =

v’ = 4.74 × 10¹⁴ Hz

Since the threshold frequency is greater than the frequency of red light, the photocell will not respond to the red light produced.