Question

If it takes 3.36 x 10^-9 J of energy to eject an electron from the surface of a certain metal, calculate the frequency of this energy and the longest possible wavelenght in nm.

Answer 1

Energy and frequency of a photon are related by E = hν, where h is Planck's constant (6.626 x 10^(-34) J s) and ν is the frequency of the photon. We have:

3.36 x 10^-19 J = 6.626 x 10^-34 Js x ν
ν = 3.36 x 10^-19 J / 6.626 x 10^-34 Js
ν = 5.07 x 10²⁴ Hz.

On the other hand, wavelength and frequency of electromagnetic radiation are related by c = λν, where c is the speed of light (3.00 x 10⁸ m/s).

So λ = c/ν = (3.00 x 10⁸ m/s) / 5.07 x 10²⁴ Hz. = 5.91x 10^-17m = 59.1x10^-18 = 59.1 a.m

( a = atto = 10^-18 )