Consider an electron moving in the first Bohr orbit of a $He^{+}$ ion with a velocity $v_1$. If it is allowed to move in the third Bohr orbit with a velocity $v_3$, then indicate the correct $v_3: v_1$ ratio.

The energy required (in $eV$) to excite an electron of $H$-atom from the ground state to the third excited state is

In the case of a hydrogen atom,when an electron falls from a higher energy level to the $M$ shell,the corresponding spectral line will form a part of:

Which of the following equations represents the velocity $(v)$ of the ejected electrons when a metal is struck with light of frequency $\nu$ and the threshold frequency of the metal is $\nu_0$? ($m_e =$ mass of electron and $h$ is Planck's constant).

Find the energy of $1$ mole of photons having a frequency of $5 \times 10^{10} \ s^{-1}$. $(h = 6.62 \times 10^{-34} \ J \ s)$

In the hydrogen atomic spectrum,a series limit is found at $12186.3 \ cm^{-1}$. To which series does it belong?