The acceleration of an electron in the first orbit of the hydrogen atom $(Z = 1)$ is

Excitation energy of a hydrogen-like ion in its first excitation state is $40.8 \, eV$. Energy needed to remove the electron from the ion in the ground state is ........ $eV$.

Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$,a neutron having thermal energy $k_B T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by $T = \frac{Z^2 h^2}{\alpha \pi^2 a_0^2 m_N k_B}$,(where $h$ is the Planck's constant,$k_B$ is the Boltzmann constant,$m_N$ is the mass of the neutron and $a_0$ is the first Bohr radius of hydrogen atom),then the value of $\alpha$ is $....$

In the lowest energy level of a hydrogen atom,the electron has an angular momentum of:

The magnetic field at the centre due to the motion of an electron in the first Bohr orbit is $B$. The magnetic field due to the motion of an electron in the second Bohr orbit at the centre will be

An orbital electron in the ground state of hydrogen has a magnetic moment $\mu_1$. This orbital electron is excited to the $3^{rd}$ excited state by some energy transfer to the hydrogen atom. If the new magnetic moment of the electron is $\mu_2$,then: