The energy of $He^{+}$ ion in its first excited state is $......eV$ (The ground state energy for the Hydrogen atom is $-13.6\,eV$).

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)

Experimentally it is found that $12.8 \, eV$ energy is required to separate a hydrogen atom into a proton and an electron. The orbital radius of the electron in this hydrogen atom is $\frac{9}{x} \times 10^{-10} \, m$. The value of $x$ is (Given: $1 \, eV = 1.6 \times 10^{-19} \, J$,$\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, Nm^2/C^2$,and electronic charge $e = 1.6 \times 10^{-19} \, C$)

For an electron moving in the $n^{\text{th}}$ Bohr orbit,the de Broglie wavelength of the electron is:

In Bohr's model of the hydrogen atom,which of the following pairs of quantities are quantized?

The magnitude of total energy and angular momentum of an electron in the $n^{th}$ orbit of a Bohr atom is denoted by $E_{n}$ and $L_{n}$ respectively. Then