The ionization potential of a hydrogen-like atom is $122.4 \, V$. Find its atomic number $Z$.

Magnetic field at the centre of a hydrogen-like atom (atomic number $= Z$) due to the motion of an electron in the $n^{th}$ orbit is proportional to

To accommodate the view that matter is made up of $5$ elements only,a scientist proposed the following hypothesis: atoms can have a maximum principal quantum number $n_{\max}$ and no higher. Then,which of the following statements must be true?

If the radius of the first Bohr orbit is $r$,then the de-Broglie wavelength of the electron in the $4^{\text{th}}$ orbit will be:

The muon has the same charge as an electron but a mass that is $207$ times greater. The negatively charged muon can bind to a proton to form a new type of hydrogen atom. How does the binding energy $E_{B\mu}$ of the muon in the ground state of a muonic hydrogen atom compare with the binding energy $E_{Be}$ of an electron in the ground state of a conventional hydrogen atom?

In a hydrogen atom,let $R$,$v$,and $E$ denote the radius,velocity,and total energy of the electron,respectively. Then,the principal quantum number $n$ is proportional to which of the following?