In hydrogen and hydrogen-like atoms,the ratio of the difference of energies $E_{4n}-E_{2n}$ and $E_{2n}-E_{n}$ varies with its atomic number $Z$ and $n$ as:

In the third orbit of a hydrogen atom,the energy of an electron is $E$. In the fifth orbit of a helium ion $(Z=2)$,the energy of an electron will be:

Explain the formulas for the energy of an electron in an atom revolving around the nucleus in different orbits.

An electron with kinetic energy $E$ collides with a hydrogen atom in the ground state. The collision will be elastic

$A$ hydrogen atom is bombarded with electrons accelerated through a potential difference of $V$, which causes excitation of hydrogen atoms. If the experiment is performed at $T = 0 \,K$, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\frac{\alpha}{10} \,V$, where $\alpha = $ . . . . . . .

An electron jumps from the $4th$ orbit to the $2nd$ orbit of a hydrogen atom. Given the Rydberg constant $R = 10^5 \text{ cm}^{-1}$. The frequency in $\text{Hz}$ of the emitted radiation will be: