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

If an electron in a hydrogen atom jumps from the third orbit to the second orbit,the frequency of the emitted radiation is given by (where $c$ is the speed of light and $R$ is the Rydberg constant):

Potential energy between a proton and an electron is given by $U = \frac{K e^2}{3 R^3}$. Then,the radius of the Bohr orbit can be given by:

Suppose in a hypothetical world, the angular momentum is quantized to be even integral multiples of $\frac{h}{2 \pi}$. According to Bohr's model, what will be the largest possible wavelength emitted by hydrogen atoms in the visible range in this world (in $\text{ nm}$)? (Consider $hc = 1242 \text{ eV-nm}$)

Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom. (in $32$ : $1$)

If the difference between the $(n+1)^{\text{th}}$ Bohr radius and the $n^{\text{th}}$ Bohr radius is equal to the $(n-1)^{\text{th}}$ Bohr radius,then find the value of $n$.