The visible range of the hydrogen spectrum contains which of the following series?

$A$ bulb of $40 \ W$ is producing light of wavelength $620 \ nm$ with $80 \%$ efficiency. The number of photons emitted by the bulb in $20 \ s$ is $(1 \ eV = 1.6 \times 10^{-19} \ J, hc = 12400 \ eV \ \mathring{A})$

Based on equation $E = -2.178 \times 10^{-18} \ J \ \frac{Z^2}{n^2}$,certain conclusions are written. Which of them is not correct?

What is the wavenumber of the photon emitted during transition from the orbit $n=5$ to that of $n=2$ in hydrogen atom (in $cm^{-1}$)?
$\left[R_{H}=109677 \ cm^{-1}\right]$

Which were the major problems before the scientists after the discovery of sub-atomic particles?

The frequency of radiation emitted when the electron falls from $n = 4$ to $n = 1$ in a hydrogen atom will be (Given $h = 6.625 \times 10^{-34} \, J s$):-