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?

Answer 1

Bohr's postulate states that the electron revolves around the nucleus only in those orbits, for which the angular momentum is some integral multiple of $\frac{h}{2\pi }$, $h$ is planck's constant $(=6.63\times {10}^{-34})$.

Thus, the angular momentum $\left(L\right)$ of the orbiting electron is quantised, i.e.,

$L=\frac{nh}{2\pi }$

Energy formula of $n^{th}$ electron,

$E_n=-\frac{13.6}{n^2}eV$

According to Bohr model, electrons having different energies belong to different levels having different values of $n$. So, their angular momentum will be different,

Hence,

$L=\frac{nh}{2\pi }$ or $L\propto n$

$\text{Final Answer}:$ No