Radius of the first orbit of the electron in a hydrogen atom is $0.53 \; \mathring{A}$. So,the radius of the third orbit will be ........... $\mathring{A}$.

The frequency of light emitted,when the electron makes a transition from the level of principal quantum number $n=2$ to the level with $n=1$ is (Take,the ionization energy of hydrogen to be $13.6 \ eV$ and $h \simeq 4 \times 10^{-15} \ eV \cdot s$)

Obtain the first Bohr's radius and the ground state energy of a muonic hydrogen atom [i.e.,an atom in which a negatively charged muon $(\mu^-)$ of mass about $207 m_{e}$ orbits around a proton].

The electron in a hydrogen atom is moving in an orbit of radius $0.53 \text{ Å}$. It takes $1.571 \times 10^{-16} \text{ s}$ to complete one revolution. The velocity of the electron will be $[\pi = 3.142]$.

The de-Broglie wavelength of the electron in the ground state of a hydrogen atom is

Let $v_{n}$ and $E_{n}$ be the respective speed and energy of an electron in the $n$th orbit of radius $r_{n}$,in a hydrogen atom,as predicted by Bohr's model. Then: