Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

Question

Consider two different hydrogen atoms. The electron in each atom is in an excited state. Is it possible for the electrons to have different energies but the same orbital angular momentum according to the Bohr model?

Philoid · Accepted Answer

From the angular momentum and energy formula of nth electron, we have,

,

Where n is nth orbit

h is Planck’s constant,

m is mass of electron

in permittivity in vacuum

and and is the angular momentum and energy of the electron in nth orbit

Clearly from above formula for orbital angular momentum and energy of orbital of electron, each n^th orbit will have unique orbital angular momentum and energies. ∴ it is not possible for electron to have different energy but same orbital angular momentum.