If the radius of the first orbit of a hydrogen atom is $5.29 \times 10^{-11} \, m$,the radius of the fourth orbit will be ......... $\mathring{A}$.

Apply Bohr's atomic model to a lithium atom. Assuming that its two $K$-shell electrons are so close to the nucleus that the nucleus and the $K$-shell electrons act as a core with an effective positive charge equivalent to $1e$. The ionization energy of its outermost electron is......$eV$.

An electron is revolving in a circular orbit of radius '$r$' in a hydrogen atom. Using Bohr's theory, the angular momentum of the electron is (where '$M$' = magnetic dipole moment,'$m$' = mass of electron,'$e$' = charge of electron).

For a hydrogen atom,when an electron jumps from $n = 2$ to $n = 1$,the wavelength of the radiation emitted is found to be $\lambda_0$. For which transition of an electron in a $He^+$ ion will the wavelength of the radiation emitted be equal to $\lambda_0$?

Mention the value of the Rydberg constant with its unit.

According to the de Broglie hypothesis,if the de Broglie wavelength of an electron in a hydrogen atom orbit of radius $5.3 \times 10^{-11} \ m$ is $10^{-10} \ m$,then the principal quantum number of the electron is ..........