Question

An electron in hydrogen atom (ground state) jumps to higher energy level x, such that potential energy of electron becomes half of its total energy at ground stste find the value of x

Answer 1

Given:

An electron in a hydrogen atom (ground state) jumps to higher energy level x, such that potential energy of electron becomes half of its total energy at ground state

To find:

Find the value of x.

Solution:

From given, we have,

The potential energy of electron becomes half of its total energy at ground state.

⇒ Total energy = Potential energy/2

An electron in a hydrogen atom (ground state) jumps to higher energy level x.

The electron energy of hydrogen atom in ground state = -13.6eV

The total energy in x excited state = -13.6/x² eV

The potential energy in x excited state = (-13.6 × 2)/x² eV

Given, the potential energy in excited state = -13.6/2 eV

∴ we have, -13.6/2 = (-13.6 × 2)/x²

x² = 4

x = √4 = 2

∴ x = 2 is the required value.