Question

The maximum kinetic energy of photoelectrons is 2.80 eV . When the wavelength of the light is increased by 50%, the maximum energy decreases to 1.30 eV . What is the work function of the cathode? What is the initial wavelength?

Answer 1

2.8 eV = 2.8 * 1.6*10^-19 J = 4.48*10^-19 Joules
1.3 eV = 2.08 * 10 ^-19 Joules.

Basic Formula  
Ek = h*c/wavelength - W
h = 6.63*10^-34
c = 3*10^8

Substitution
First condition
4.48 * 10^-19 J = hc/wavelength - W
Second Condition
2.08* 10^-19 J = hc/1.5 wavelength - W Subtract these two conditions.

Find the wavelength
(4.48 - 2.08)*10^-19 = hc/wavelength [ 1 - 1/1.5]

wavelength = hc/2.4*10^-19 [1/3]

wavelength = 6.63*10^-34 * 3*10^8/2.4* 10^-19 * [1/3]

wavelength = 2.76* 10^-7 meters.

Find the Work Function
2.8*1.6*10^-19 = hc/wavelength - W
2.8*1.6*10^-19 = 6.63*10^-34 * 3*10^8 / 2.76*10^-7 - w
4.48*10^-19 = 7.20 * 10^-19 - W
- 3.67*10^-19 = - W
W = 2.73*10^19 J
W = 2.73*10^-19 / 1.6 * 10^-19 = 1.7eV
Using .. hf = Φ + ½mv²

(1) h(c/λ) = Φ + 1.7eV
(2) h(c/1.5λ) = Φ + 1.3eV
Equation

1 - 2
h(c/λ)[1 - 1/1.5] = .4eV
h(c/λ)[0.3333] = .4eV
λ = 0.3333*hc/(.4*1.60E-19 J) =

use (1) h(c/λ) = Φ + (2.8*1.60E-19 J)
Φ = 3.68E-19 J
Check calculation again there may be some mistake in calculation