What is the radius of Bohr's fifth orbit for $B^{+4}$ in $\mathring{A}$ (in $.645$)?

The wave number of the first emission line in the Balmer series of the $H$ atom spectrum will be .......

The energy of an electron in an orbit of a hydrogen-like ion with an orbit radius of $52.9 \ pm$ in $J$ is (ground state energy of an electron in a hydrogen atom is $-2.18 \times 10^{-18} \ J$).

The ratio of the radius of the second orbit of $Li^{2+}$ to that of the third orbit of $Be^{3+}$ is:

The threshold frequency $v_{0}$ for a metal is $7.0 \times 10^{14} \,s^{-1}.$ Calculate the kinetic energy of an electron emitted when radiation of frequency $v = 1.0 \times 10^{15} \,s^{-1}$ hits the metal.

For a $H$ atom,the wavelength for the highest energy transition is $91.2 \ nm$. Calculate the corresponding wavelength for $He^{+}$ in $nm$.