With a 2-fold decrease in the wavelength of light incident on a metal plate, the maximum kinetic

With a 2-fold decrease in the wavelength of light incident on a metal plate, the maximum kinetic energy of electrons increased by a factor of 3. Determine the work function of electrons if the initial photon energy was 10 eV.

Let’s write down the Einstein equation for the photoelectric effect:
h * ν = A + T, where A is the work function of the electron from the metal, T is the kinetic energy of photoelectrons, h is Planck’s constant h = 6.63 * 10 ^ -34 J * s, ν is the radiation frequency.
The radiation frequency is found from the expression:
ν = c / λ, where c is the speed of light, λ is the wavelength.
h * ν – energy of photons.
Substitute all of this into Einstein’s equation:
h * s / λ = A + T
Initially:
10 = A + T
After the change:
h * s / (λ / 2) = 2 * h * s / λ
2 * 10 = A + 3 * T
Let us express T from the original and substitute in after the change:
T = 10 – A
2 * 10 = A + 3 * T = A + 3 * (10 – A) = A + 30 – 3 * A = 30 – 2A
A = 30-20 / 2 = 5 eV.
Answer: the work function of electrons is 5 eV.