The energy of an electron in an orbit of a hydrogen-like ion with an orbit radius of $52.9 \ pm$ in $J$ is (ground state energy of an electron in a hydrogen atom is $-2.18 \times 10^{-18} \ J$).

In a hydrogen atom,electrons are excited to the $5^{th}$ quantum level. How many different spectral lines may appear in the emission spectrum?

The wavenumber of the first line $(n_2=3)$ in the Balmer series of hydrogen is $\bar{\nu}_1 \ cm^{-1}$. What is the wavenumber (in $cm^{-1}$) of the second line $(n_2=4)$ in the Balmer series of $He^{+}$?

The work functions (in $eV$) of $Mg, Cu, Ag, Na$ respectively are $3.7, 4.8, 4.3, 2.3$. From how many metals,the electrons will be ejected if their surfaces are irradiated with an electromagnetic radiation of wavelength $300 \ nm$ ?
$(h=6.6 \times 10^{-34} \ Js, 1 \ eV=1.6 \times 10^{-19} \ J)$

In a hydrogen atom, an electron is transferred from an orbit of radius $1.3225 \ nm$ to another orbit of radius $0.2116 \ nm$. What is the energy (in $J$) of the emitted radiation?

If the energies of two light radiations $E_1$ and $E_2$ are $25 \ eV$ and $100 \ eV$ respectively,then their respective wavelengths $\lambda_1$ and $\lambda_2$ would be in the ratio $\lambda_1: \lambda_2=$