The triply ionized beryllium ($\text{Be}^{+++}$) has the same electron orbital radius as that of the ground state of hydrogen. Hence, the energy state of triply ionized beryllium is (Given $Z = 4$ for beryllium)

The angular momentum of the electron in the third Bohr orbit of a hydrogen atom is '$l$' so its angular momentum in the fourth Bohr orbit is

In Bohr's atomic model, the energy of the electron is 'E' in the second orbit of hydrogen atom. So the energy of the electron in the third orbit of helium atom $(Z = 2)$ will be

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t = 0$ and $\dfrac{N_0}{e}$ counts per minute at time $t = 3$ minute. The time (in minute) in which the activity reduces to half the value, is