The energy of an electron in the $3^{rd}$ orbit of a hydrogenic atom is $-E$. The energy of an electron in the first orbit will be

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

When a metal surface is irradiated with light of frequency $x \ Hz$,the kinetic energy of emitted photoelectrons is $z \ J$. When the same metal is irradiated with light of frequency $y \ Hz$,the kinetic energy of emitted electrons is $\frac{z}{3} \ J$. What is the threshold frequency (in $Hz$) of the metal?

If the work function for the photoelectron emission of a metal is $3.75 \ eV$,then the threshold wavelength of the radiation needed for the ejection of the electron is approximately (in $nm$)

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is

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: $h = 6.6 \times 10^{-34} \ J \ s$,$N_A = 6.02 \times 10^{23} \ mol^{-1}$)