The hydrogen atom in the ground state has an energy of Е1 = -13.55 eV. If, when a photon is emitted

The hydrogen atom in the ground state has an energy of Е1 = -13.55 eV. If, when a photon is emitted, an atom passes from the third energy level to the first, then the wavelength of the emitted photon is?

The energy of an electron in a hydrogen atom at a level numbered (n is the principal quantum number):

En = (-13.6 eV) / n ^ 2;

E3 = (-13.6 eV) / 3 ^ 2 = (-13.6 / 9) eV = -1.51 eV.

In accordance with Bohr’s 2nd postulate, the radiation frequency during the transition from the 3rd level to the 1st is determined by the formula:

hν = E3 – E1;

ν = (E3 – E1) / h = (-1.51 eV – (-13.6 eV)) / (4.136 * 10 ^ -15 eV * s) =

= (12.09 eV) / (4.136 * 10 ^ -15 eV * s) = 2.92 * 10 ^ 15 s-1.

Wavelength λ:

λ = s / ν = (3 * 10 ^ 8 m / s) / (2.92 * 10 ^ 15 s-1) = 1.027 * 10 ^ -7 m.

Answer: 1.027 * 10 ^ -7 m.