Question

Given the following data for incident wavelength and the stopping potential obtained from an experiment on photoelectric effect, estimate the value of Planck’s constant and the work function of the cathode material.

What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?

Incident wavelength (in Å)	2536	3650
Stopping potential (in V)	1.95	0.5

Answer 1

Data: λ = 2536Å = 2.536 × 10^-7 m, 

λ’ = 3650Å = 3.650 ×10^-7 m, V_o = 1.95V, V_o ‘ = 0.5V, 

c = 3 × 10⁸ m/s, e = 1.6 × 10^-19 C

(i) V_oe = \(\cfrac{hc}{\lambda}\) – Φ and V_o ‘e = \(\cfrac{hc}{\lambda'}\) - Φ

∴ (V_o – V_o‘)e = hc \((\cfrac{1}{\lambda}-\cfrac{1}{\lambda'})\)

∴ (1.95 – 0.5) (1.6 × 10^-19)

This is the value of Planck’s constant.

(ii) Φ = \(\cfrac{hc}{\lambda}\) - V_oe

This is the work function of the cathode material.

(iii) Φ = hv_o

∴ The threshold frequency, v_o = \(\cfrac{\phi}h\)

= \(\cfrac{4.484\times10^{-19}J}{6.428\times10^{-34}J{.s}}\) = 6.976 x 10¹⁴ HZ

(iv) v_o = \(\cfrac{c}{\lambda_o}\)

∴ The threshold frequency, λ_o = \(\cfrac{c}{v_o}\)

= \(\cfrac{3\times10^8}{6.976\times10^{14}}\) = 4.300 × 10^-7 m = 4300 Å

(v) The most likely metal used for emitter : calcium