The emission spectrum of a gaseous atom is line-based and not continuous. Why?

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

Which are the drawbacks of Rutherford's atomic model?

If the velocity of the revolving electron of $He^{+}$ in the first orbit $(n=1)$ is $v$,what is the velocity of the electron in the second orbit $(n=2)$?

The energy of the orbit of hydrogen is $E_n = \frac{1.31 \times 10^6}{n^2} \ J \ mol^{-1}$. If an electron transits from $n = 3$ to $n = 2$,find the frequency of the emitted radiation. (Note: $h = 6.6 \times 10^{-34} \ J \ s$,$N_A = 6.02 \times 10^{23} \ mol^{-1}$)

The deflection of a few $\alpha$-particles when bombarded on a thin gold foil indicates that $.......$