Question

The electron in a hydrogen atom is in the first excited state, when the electron acquires an additional 2.86 eV of energy. What is the quantum number of the state into which the electron moves?

a. 1

b. 2

c. 3

d. 4

e. 5

Answer 1

e) 5

here is the explantion:

Energy in 1st excited state, E2 = 13.6/2^2

= 3.4 eV

Energy in 2nd ecited state, E3 = 13.6/3^2

= 1.51 eV

Energy in 3rd ecited state, E4 = 13.6/4^2

= 0.85 eV

Energy in 4th excited state, E5 = 13.6/5^2

= 0.54 eV

clearly Energy received by elelctron , E = E1 - E5

E1-E5 = 3.4 - 0.54

= 2.86 eV

so, electron goes to 4th excited state, n = 5