Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.

The existence of a positively charged nucleus was established by:

The ground and first excited state energies are $E_1$ and $E_2$ respectively. Which pair of species has the same energy? [Note that energy is indicated in the bracket].

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?

The value of Planck's constant is $6.63 \times 10^{-34} \ J \ s$. The speed of light is $3 \times 10^{17} \ nm \ s^{-1}$. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of $6 \times 10^{18} \ s^{-1}$?

The angular momentum of an electron in a given orbit is $J$. Its kinetic energy will be: