Question

A photon of energy 12.4 eV is completely absorbed by a hydrogen atom initially in the ground state so that it is excited. The quantum number of the excited state is

• A. n =1
• B. n = 3
• C. n = 4
• D. n = ∞

Answer 1

Answer: (C)

n = 4

Answer 2

Let electron absorbing the photon energy reaches to the excited state n. Then using energy conservation

⇒ $- \frac{13.6}{n^{2}} = - 13.6 + 12.4$ ⇒ $- \frac{13.6}{n^{2}} = - 1.2$

⇒ $n^{2} = \frac{13.6}{1.2} = 12$ ⇒ n = 3.46 ≃ 4