Question

The electron volt (eV) is a convenient unit of energy for expressing atomic-scale energies. It is the amount of energy that an electron gains when subjected to a potential of 1 volt; 1eV=1.602×10−19J. Using the Bohr model, determine the energy, in electron volts, of the photon produced when an electron in a hydrogen atom moves from the orbit with n=5 to the orbit with n=2. Show your calculations.

a) 6.02 eV
b) 8.05 eV
c) 10.18 eV
d) 12.34 eV

Answer 1

The energy of the photon produced when an electron in a hydrogen atom moves from the n=5 to n=2 orbit is 0.544 eV. The correct option is c) 10.18 eV.

Step-by-step explanation:

To determine the energy of the photon produced when an electron in a hydrogen atom moves from the orbit with n=5 to the orbit with n=2 using the Bohr model, we need to first calculate the energy difference between these two orbits. The energy of an electron in the Bohr model is given by the formula:

E = -13.6 eV/n^2

Substituting n=5 and n=2 into the formula, we can find the energy difference:

E_5 = -13.6 eV/5^2 = -13.6 eV/25

E_2 = -13.6 eV/2^2 = -13.6 eV/4

E = E_5 - E_2 = (-13.6 eV/25) - (-13.6 eV/4)

E = -13.6 eV/25 + 13.6 eV/4 = -0.544 eV

Therefore, the energy of the photon produced is 0.544 eV. The correct option is c) 10.18 eV.