What is the wave number of the lowest energy transition in the Balmer series?

Supposing the energy of the fourth shell for a hydrogen atom is $-25 \, a.u.$ (arbitrary unit). What would be its potential energy in the ground state?

When an electron jumps from $n = 5$ to $n = 2$ with all possible transitions,which of the following statements is correct?

The longest wavelength line in the Lyman series of the $H$ atom spectrum is $:-$

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate $(a)$ threshold wavelength and $(b)$ Planck's constant.

$\lambda \ (nm)$	$500, 450, 400$
$v \times 10^{-5} \ (cm \ s^{-1})$	$2.55, 4.35, 5.35$

In astronomical observations,signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} \, J$ from the radiations of $600 \, nm$,calculate the number of photons received by the detector.