The radius of the third stationary orbit of an electron for a Bohr atom is $R$. The radius of the fourth stationary orbit will be

The ionization potential of a hydrogen-like atom is $122.4 \, V$. Find its atomic number $Z$.

Suppose an electron is attracted towards the origin by a force $F = \frac{k}{r}$,where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying the Bohr model to this system,the radius of the $n^{th}$ orbital of the electron is found to be $r_n$ and the kinetic energy of the electron is $K_n$. Then which of the following is true?

The energy of a hydrogen atom in the ground state is $-13.6 \, eV$. The energy of the $He^+$ ion in the first excited state will be .... $eV$.

$A$ monochromatic radiation of wavelength $\lambda$ is incident on a hydrogen sample in ground state. The sample subsequently emits radiation of six different wavelengths, then the value of $\lambda$ is. [Use $hc = 1242 \text{ eV-nm}$] (in $\text{ nm}$)

An electron revolving in the $n^{\text{th}}$ Bohr orbit has a magnetic moment $\mu_n$. If $\mu_n \propto n^x$,the value of $x$ is: