The de Broglie wavelength of the electron in the ground state is $\lambda_1$ and that in the $n = 3$ level is $\lambda_3$ then $\lambda_3$ is given by

If the difference between $(n + 1)^{th}$ Bohr radius and $n^{th}$ Bohr radius is given by $(n - 1)^{th}$ Bohr radius, then the value of n is

Two samples A and B contain equal amount of radioactive substances. If $\left(\dfrac{1}{8}\right)^{th}$ of sample A and $\left(\dfrac{1}{128}\right)^{th}$ of sample B, remain after 9 hours, then the ratio of half life period of B to that of A is

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)