The series limit for the frequency of Balmer series is ' $\mathrm{v}_{\mathrm{B}}$ ', then the series limit frequency of Paschen series ' $v_p$ ' is

Radioactive materials A and B have decay constants ' $9 \lambda$ ' and ' $\lambda$ ' respectively. Initially they have same number of nuclei. The ratio of number of nuclei of material ' $A$ ' to that of ' $B$ ' will be $\left(\frac{1}{\mathrm{e}}\right)$ after time ' $t$ '. So ' $t$ ' is equal to

If $R_1$ and $R_2$ are the radii of the atomic nuclei of mass numbers 27 and 125 respectively, then the ratio $R_2: R_1$ is

The angular momentum of electron in hydrogen atom in first orbit is ' $L$ '. The change in angular momentum if electron is in second orbit of hydrogen atom is