Question

In an X-ray photoelectron experiment, a photon of wavelength λ=1.50 Å (1 Å = 10^-10 m) ejects an electron from the inner shell of an atom, and the electron emerges with a velocity of 2.14 x 10^7 m/s. What is the binding energy [in electron volts (eV)] of the electron in the atom?

Answer 1

Energy of photon = hν = hc/λ =

Where h = planck's constant

c = speed of light

λ = wavelength

Energy = (6.626×10^-34 Js)×(3×10⁸ m / s) / 1.5 X 10^-10 m = 13.252 X 10^-16 Joules

The energy will be absorbed by electon and will have velocity = 2.14 x 10^7 m/s

so rest of energy will be the binding energy

LEt us calcualte the kinetic energy of electron

Kinectic energy = 1/2 X mass X (velocity of electron)^2 = 1/2 X 9.11×10^-31 kg X (2.14 x 10^7 )^2

Kinetic energy = 20.86 X 10^-17 Joules

So binding energy = 13.252 X 10^-16 Joules - 20.86 X 10^-17 Joules = 11.17 X 10^-16 joules

1 joules = 6.242 X 10^18 ev

So 11.17 X 10^-16 joules = 11.17 X 10^-16 X 6.242 X 10^18 ev = 69.72 X 10^2 ev