Question

The energy of an electron in a hydrogen atom in ground state is −13.6 eV. Its energy in an orbit corresponding to quantum number n is −0.544 eV. The value of n is ______.

Options

• 2

• 3

• 4

• 5

Answer 1

The energy of an electron in a hydrogen atom in ground state is −13.6 eV. Its energy in an orbit corresponding to quantum number n is −0.544 eV. The value of n is 5.

Explanation:

Given: E_n = −0.544 eV

The energy of an electron in a hydrogen atom is given by the formula:

E_n = `(-13.6)/n^2` eV

−0.544 = `(-13.6)/n^2`

n² = `13.6/0.544`

n² = 25

n = `sqrt 25`

n = 5