Calculate the maximum speed of electrons ripped out of metal by light with a wavelength of 0.18 microns.

Calculate the maximum speed of electrons ripped out of metal by light with a wavelength of 0.18 microns. The work function is 7.2 * 10-19 J.

We translate the values ​​from given to SI:
λ = 0.18 μm = 0.18 * 10 ^ -6 m.
1. 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.
2. Maximum kinetic energy
Tmax = m * vmax² / 2, where m is the electron mass m = 9.1 * 10 ^ -31 kg, vmax is the maximum electron speed.
3. The radiation frequency is found from the expression:
ν = c / λ, where c is the speed of light c = 3 * 10 ^ 8 m / s, λ is the wavelength.
4. Substituting everything into the formula for the photoelectric effect, we get:
h * s / λ = A + m * vmax² / 2
Hence:
vmax = √ ((2 / m) * (h * s / λ – A))
5. Substitute the numbers and determine the maximum electron velocity:
vmax = √ ((2 / m) * (h * s / λ – A)) = √ ((2 / 9.1 * 10 ^ -31) * (6.63 * 10 ^ -34 * 3 * 10 ^ 8 / 0.18 * 10 ^ -6 – 7.2 * 10 ^ -19)) = 0.92 * 10 ^ 6 m / s
Answer: the maximum electron speed is 0.92 * 10 ^ 6 m / s or 0.92 Mm / s.