Angular momentum of an electron in a hydrogen atom is $\frac{3h}{2\pi}$ ($h$ is the Planck's constant). The kinetic energy $(KE)$ of the electron is (in $\text{ eV}$)

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,show that this frequency equals the classical frequency of revolution of the electron in the orbit.

Suppose an electron in an atom experiences an attractive force towards the nucleus given by $F = k/r$,where $k$ is a constant and $r$ is the distance of the electron from the nucleus. Applying the Bohr model to this system,the radius of the $n^{th}$ orbit $r_n$ and the kinetic energy of the electron in that orbit $K_n$ are found. Which of the following relationships is correct?

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of the electron (in $\%$)?

$A$ hydrogen atom in its ground state absorbs $10.2 \ eV$ of energy. The orbital angular momentum is increased by (Given Planck constant $h = 6.6 \times 10^{-34} \ J \cdot s$)

The number of absorption transitions between the first and the fourth energy states of a hydrogen atom is $3$. The number of emission transitions between these states will be