NCERT Solutions for Chapter: Atoms, Exercise 3: SA

Positronium is just like a $\mathrm{H}$-atom with the proton replaced by the positively charged anti-particle of the electron (called the positron which is as massive as the electron). What would be the ground state energy of positronium?

Assume that there is no repulsive force between the electrons in an atom but the force between positive and negative charges given by Coulomb’s law as usual. Under such circumstances, calculate the ground state energy of a He-atom.

Using Bohr model, calculate the electric current created by the electron when the H-atom is in the ground state.

Show that the first few frequencies of light that is emitted when electrons fall to the $n^{th}$ level from levels higher than $n$ are approximate harmonics (i.e. in the ratio $1:2:3$) when $n>>1$.

What is the minimum energy that must be given to a H atom in ground state so that it can emit an $H_{\gamma }$ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such $H_{\gamma }$ photon?