What is the radius of the stationary orbits $(n)$? State the formula.

Supposing the energy of the fourth shell for a hydrogen atom is $-25 \, a.u.$ (arbitrary unit). What would be its potential energy in the ground state?

What is the ratio of the time period of revolution of an electron in the second orbit of a hydrogen atom to that in the third orbit of a $He^{+}$ ion?

The angular momentum of an electron in an $H$ atom in a particular $n$ state is $\frac{h}{\pi}$. What is the energy in $J$ required to excite the electron from this particular $n$ state to $(n+1)$ state? $(x = 2.18 \times 10^{-18} \ J)$

The radius of the first excited state of a Helium ion $(He^+)$ is given by (where $a_0$ is the radius of the first stationary state of the hydrogen atom):

$A$ source of monochromatic radiation of wavelength $400 \, nm$ provides $1000 \, J$ of energy in $10 \, seconds$. When this radiation falls on the surface of sodium,$x \times 10^{20}$ electrons are ejected per second. Assume that wavelength $400 \, nm$ is sufficient for ejection of electrons from the surface of sodium metal. The value of $x$ is $......$. (Nearest integer) $(h = 6.626 \times 10^{-34} \, Js)$