Calculate the energy of $1 \ mol$ of photons having a frequency of $4.0 \times 10^{14} \ Hz$.

The $\alpha$-particle scattering experiment of Rutherford concluded that

Explain the following according to Bohr's model of hydrogen:
$(i)$ Principal quantum number
$(ii)$ Radius of stationary orbit $(r)$
$(iii)$ Energy of stationary state
$(iv)$ Isoelectronic ion of $H$
$(v)$ Velocity of electron

For the hydrogen emission spectrum,the energy change $E$ (in Joules) is given by $\Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \ J$,where $n_1 = 1, 2, 3, \dots$ and $n_2 = 2, 3, 4, \dots$. Which of the following corresponds to the Paschen series?

Calculate the ionization energy of $H$,$He^{+}$,and $Li^{2+}$ in $kJ \, mol^{-1}$.

$A$ certain metal has a work function of $\Phi = 2 \ eV$. It is irradiated first with $1 \ W$ of $400 \ nm$ light and later with $1 \ W$ of $800 \ nm$ light. Among the following,the correct statement is
[Given: Planck constant $(h) = 6.626 \times 10^{-34} \ J \ s$;
Speed of light $(c) = 3 \times 10^8 \ m \ s^{-1}$ ]