Question

Given the following data for incident wavelength and the stopping potential obtained from an experiment on the 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 = 2536 Å = 2.536 × 10^-7 m, 
λ' = 3650 Å = 3.650 × 10^-7 m,
V₀ = 1.95 V, V₀' = 0.5 V, c = 3 × 10⁸ m/s,
e = 1.6 × 10^-19 C

(i) `"V"_0"e" = "hc"/lambda - phi and "V"_0'"e" = "hc"/(lambda') - phi`

∴ `("V"_0 - "V"_0')"e" = "hc" (1/lambda - 1/(lambda '))`

∴ (1.95 - 0.5)(1.6 × 10^-19)

= h (3 × 10⁸)`(10^7/2.536 - 10^7/3.650)`

∴ 2.32 × 10^-19 = h(3 × 10¹⁵)(0.3943 - 0.2740)

∴ h = `(2.32 xx 10^(-34))/0.3609 = 6.428 xx 10^(-34)` J.s

This is the value of Planck's constant.

(ii) `phi = "hc"/lambda - "V"_0"e"`

`= ((6.428 xx 10^-34)(3 xx 10^8))/(2.536 xx 10^-7) - (1.95)(1.6 xx 10^-19)`

`= 7.604 xx 10^-19 - 3.12 xx 10^-19 = 4.484 xx 10^-19`J

`= (4.484 xx 10^-19"J")/(1.6 xx 10^-19 "J"//"eV")`

= 2.803 eV

This the work function of the cathode material.

(iii) Φ = hv₀

∴ The threshold frequency, `"v"_0 = phi/"h"`

`= (4.484 xx 10^-19 "J")/(6.428 xx 10^-34 "J.s") = 6.976 xx 10^14` Hz

(iv) `"v"_0 = "c"/lambda_0`

∴ The threshold wavelength, `lambda_0 = "c"/"v"_0`

`= (3 xx 10^8)/(6.976 xx 10^14) = 4.300 xx 10^-7` = 4300 Å

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