If the radius of the first Bohr orbit in a hydrogen atom is $0.53 \, \mathring A$,then the radius of the third Bohr orbit will be ....... $\mathring A$.

In any Bohr orbit of the hydrogen atom,the ratio of kinetic energy to potential energy of the electron is

The ionization potential for the second $He$ electron is ...... $eV$.

In the Auger process,an atom makes a transition to a lower state without emitting a photon. The excess energy is transferred to an outer electron which may be ejected by the atom. (This is called an Auger electron). Assuming the nucleus to be massive,calculate the kinetic energy of an $n = 4$ Auger electron emitted by Chromium by absorbing the energy from an $n = 2$ to $n = 1$ transition.

$A$ particle of mass $200 \, MeV/c^2$ collides with a hydrogen atom at rest. Soon after the collision,the particle comes to rest,and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in $eV$) is $\frac{N}{4}$. The value of $N$ is: (Given the mass of the hydrogen atom to be $1 \, GeV/c^2$)

The magnetic moment $(m_{orb})$ of a revolving electron around the nucleus varies with the principal quantum number $(n)$ as