Question

A ground state hydrogen atom absorbs a photon of wavelength 94.98 nm and its electron attains a higher energy level. The atom then emits two photons: one of wavelength 1282.2 nm to reach an intermediate level and a second to return to the ground state. What was the wavelength of the second photon emitted?

Answer 1

Answer: 102.63 nm

Explanation: In order to explain this problem we have to considerer the Plack postulate for the energy of the photons given by:

E=h*c/λ where H and c are the Planck constant and speed of light.

E=1240 nm*eV/94.98 nm= 13.05 eV

Then we have a first emitted photon with a wavelength of 1282.2 nm so  its energy is;

Einter=1240/1282.2=0.97 eV

so the energy to get the ground state from this level is

E=(13.05-0.97)=12.08 eV

From this level, the second  emitted photon has a wavelength given by:

λ=1240/12.08=102.65 nm