In a hypothetical Bohr hydrogen atom, if the mass of the electron is doubled, then the energy of the electron in the first orbit is: (in $\text{ eV}$)

In a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?

The angular momentum of an electron in a hydrogen atom is proportional to: (Where $r$ is the radius of the orbit of the electron)

Given below are two statements:
Statement $I$: In a hydrogen atom,the frequency of radiation emitted when an electron jumps from a lower energy orbit $(E_1)$ to a higher energy orbit $(E_2)$ is given as $hf = E_1 - E_2$.
Statement $II$: The jumping of an electron from a higher energy orbit $(E_2)$ to a lower energy orbit $(E_1)$ is associated with the frequency of radiation given as $f = (E_2 - E_1) / h$.
This condition is Bohr's frequency condition. In the light of the above statements,choose the correct answer from the options given below.

The ratio of the speed of an electron in the ground state of the Bohr's first orbit of a hydrogen atom to the velocity of light in air is:

When a hydrogen atom is in its first excited level,its radius is .... of the Bohr radius.