The radius of a hydrogen atom in its ground state is $5.3 \times 10^{-11} \ m$. After collision with an electron,it is found to have a radius of $21.2 \times 10^{-11} \ m$. What is the principal quantum number $n$ of the final state of the atom?

$A$ $\mu$-meson of charge '$e$',mass $208 m_e$ moves in a circular orbit around a heavy nucleus having charge $+3e$. The quantum state '$n$' for which the radius of the orbit is the same as that of the first Bohr orbit for a hydrogen atom is [approximately]:

In the Bohr model of the hydrogen atom,the centripetal force is provided by the Coulomb attraction between the proton and the electron. If $r_0$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and $\varepsilon_0$ is the permittivity of vacuum,the speed of the electron is:

According to the classical electromagnetic theory,calculate the initial frequency of the light emitted by the electron revolving around a proton in a hydrogen atom.

The Hitomi satellite recently observed the Lyman alpha emission line ($n=2$ to $n=1$) of hydrogen-like iron ion (atomic number of iron is $26$) from the Perseus galaxy cluster. The wavelength of the line is closest to ............... $\mathring{A}$.

If the radius of the first orbit of an $H$ atom is $a_0$, then the de Broglie wavelength of an electron in the third orbit is: (in $\pi a_0$)