The work function of an electron from zinc is 4 eV. What is the kinetic energy of photoelectrons

The work function of an electron from zinc is 4 eV. What is the kinetic energy of photoelectrons when illuminated with zinc plastite radiation with a wavelength of 200 nm?

We give all the values ​​from given in the SI system:
A = 4 eV = 4 * 1.6 * 10 ^ -19 J = 6.4 * 10 ^ -19 J.
λ = 200 nm. = 200 * 10 ^ -9 m.
Let’s write down the Einstein equation for the photoelectric effect:

h * ν = A + Tmax, where A is the work function of an electron from the metal, Tmax is the maximum 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.

Let’s substitute all of this in Einstein’s equation:
h * s / λ = A + Tmax
Let us express Tmax from this expression:
Tmax = h * s / λ – A
Substitute the numerical values ​​and determine the kinetic energy:
Tmax = h * s / λ – A = 6.63 * 10 ^ -34 * 3 * 10 ^ 8/200 * 10 ^ -9 – 6.4 * 10 ^ -19 = 3.545 * 10 ^ -19 J.
Answer: the kinetic energy of photoelectrons is 3.545 * 10 ^ -19 J. or 2.21 eV.