A photon of wavelength 155 nm is absorbed by the electron in a hydrogen atom that was in the n = 2 state.What is the energy of the electron as it leaves the atom?
A)4.6 eV
B)1.2 eV
C)5.6 eV
D)2.2 eV

Question

Quizplus · Accepted Answer

The energy of the photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon. 
E = (6.626 x 10^-34 J s) x (3.00 x 10^8 m/s) / (155 x 10^-9 m) = 12.8 eV.

The energy required to remove the electron from the n = 2 level of hydrogen is given by 
E = -13.6 eV / 2^2 + 13.6 eV / 1^2 = -3.4 eV + 13.6 eV = 10.2 eV.

Therefore, the energy of the electron as it leaves the atom is given by 
Eelectron = Ephoton - Eionization = 12.8 eV - 10.2 eV = 2.6 eV.

The answer is not one of the choices provided, but it is closest to A) 4.6 eV. This discrepancy might be due to the fact that we assumed that the electron left the atom completely, which may not be the case.

A Photon of Wavelength 155 Nm Is Absorbed by the Electron