What will be the energy of an electron emitted from the ground state to the $n^{th}$ orbit?

An electron in an atom jumps in such a way that its kinetic energy changes from $x$ to $\frac{x}{4}$. The change in potential energy will be

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):

Neon gas is generally used in sign boards. If it emits strongly at $616 \, nm$,calculate $(a)$ the frequency of emission,$(b)$ distance traveled by this radiation in $30 \, s$,$(c)$ energy of a quantum,and $(d)$ number of quanta present if it produces $2 \, J$ of energy.

How many spectral lines are obtained when an electron in a hydrogen atom undergoes a transition from the $7^{th}$ Bohr orbit to the $2^{nd}$ orbit?

Give names of atomic models and write about Thomson model.