Angular momentum of an electron in the $M$-shell of a $Li^{+2}$ ion is:

The energy (in $J$) released when an excited electron of the $5^{th}$ orbit of a hydrogen atom returns to its ground state is

$(i)$ What is the energy of an electron for hydrogen in $J \ atom^{-1}$ and $J \ mol^{-1}$?
$(ii)$ Calculate the energy of this electron per mole for the first transition ($n=1$ to $n=2$).
$(iii)$ Calculate the ionization energy of hydrogen.

The value of Planck's constant is $6.63 \times 10^{-34} \, J \cdot s$ and the speed of light is $3.0 \times 10^8 \, m \cdot s^{-1}$. The wavelength of a quantum of light with a frequency of $8 \times 10^{15} \, s^{-1}$ is closest to which of the following values in meters?

The wave number of the first line of the Balmer series in the hydrogen spectrum is $15200 \, cm^{-1}$. What will be the wave number of the first line of the Balmer series for the $Li^{2+}$ ion in $cm^{-1}$?

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $\frac{h^{2}}{xma_{0}^{2}}$. The value of $10x$ is ........ . ($a_{0}$ is radius of Bohr's orbit) (Nearest integer) [Given : $\pi=3.14$]