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

In Bohr's model of the hydrogen atom,let $PE$ represent potential energy and $TE$ represent total energy. When an electron transitions to a higher energy level,

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?

What is the number of de Broglie wavelengths associated with an electron revolving in the $n^{th}$ allowed orbit of a Bohr atom?

In Bohr's model of the hydrogen atom,the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is

Considering the Bohr model of hydrogen-like atoms,the ratio of the radius of the $5^{\text{th}}$ orbit of the electron in $Li^{2+}$ to that in $He^{+}$ is: