$A$ particular hydrogen-like ion emits radiation of frequency $2.92 \times 10^{15} \text{ Hz}$ when it makes a transition from $n=3$ to $n=1$. The frequency in $\text{Hz}$ of radiation emitted in the transition from $n=2$ to $n=1$ will be: (in $\times 10^{15}$)

Given below are two statements.
Statement $(I) :$ The dimensions of Planck's constant and angular momentum are same.
Statement $(II) :$ In Bohr's model,electrons revolve around the nucleus only in those orbits for which angular momentum is an integral multiple of Planck's constant.
In the light of the above statements,choose the most appropriate answer from the options given below.

What is the angular momentum of an electron in Bohr's hydrogen atom whose energy is $-3.4 \,eV$?

Which of the following graphs in the figure shows the speed $(v)$ of an electron in a hydrogen atom as a function of the principal quantum number $(n)$?

$A$ $15.0\, eV$ photon collides with and ionizes a hydrogen atom. If the atom was originally in the ground state (ionization potential $= 13.6\, eV$),what is the kinetic energy of the ejected electron? .......... $eV$

Hydrogen $(H)$,deuterium $(D)$,singly ionized helium $(He^+)$ and doubly ionized lithium $(Li^{2+})$ all have one electron around the nucleus. Consider the $n = 2$ to $n = 1$ transition. The wavelengths of emitted radiations are $\lambda_1, \lambda_2, \lambda_3$ and $\lambda_4$ respectively. Then approximately: