The difference between the $n^{th}$ and $(n+1)^{th}$ Bohr radius of an $H$ atom is equal to its $(n-1)^{th}$ Bohr radius. The value of $n$ is:

What is the ratio of the wavelengths emitted during the $2 \to 1$ transition in $Li^{++}$,$He^+$,and $H$?

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.

The de Broglie wavelength of the electron in the ground state is $\lambda_1$ and that in the $n = 3$ level is $\lambda_3$. Then $\lambda_3$ is given by:

In Bohr's theory of the hydrogen atom,'$r$' is the radius of the orbit,'$V$' is the speed of the electron, and '$E$' is the total energy of the electron. Which of the following physical quantities is inversely proportional to the principal quantum number '$n$'?

Kinetic energy of the electron in a hydrogen atom is $\frac{e^{2}}{8 \pi \varepsilon_{0} r}$. Then its potential energy is . . . . . . .