Two series of spectral lines of atomic hydrogen which do not belong to the infrared spectral region are

$A$ metal having a work function of $4 \, eV$ is exposed to a photon of $\lambda = 1240 \, \mathring{A}$. If an accelerating potential of $7.6 \, V$ is applied,then the electron with maximum kinetic energy will have a speed equal to -

According to Bohr's model,the energy of an electron is given by $E = -\frac{2.176 \times 10^{-18}}{n^2} \, J \, atom^{-1}$. Calculate the minimum energy required to remove an electron from the $3^{rd}$ orbit of a $He^{+}$ ion,and also calculate the corresponding wavelength of the photon.

If $n=2$ for $He^{+}$ ion,then what is the wavelength in $\mathring{A}$?

The energy of an electron in the first Bohr orbit of a hydrogen atom is $-13.12 \times 10^5 \ J \ mol^{-1}$. Calculate the energy required for the transition of an electron from the first orbit to the second orbit.

Calculate the ratio of the radius of the $2^{nd}$ and $3^{rd}$ orbit of a hydrogen atom. (Note: $r_n \propto n^2$)