A radioactive element having half-life 30 min . is undergoing beta decay. The fraction of radioactive element remains undecayed after 90 min . will be

The ratio of the total energy of the $2^{\text {nd }}$ orbit electron for the hydrogen atom ($^1\mathrm{H}$) to that of a helium ion ($\mathrm{He}^+$) is :

The magnetic moment of electron due to orbital motion is proportional to ( $\mathrm{n}=$ principal quantum number)

The frequencies for series limit of Balmer and Paschen series are ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_3$ ' respectively. If frequency of first line of Balmer series ' $\mathrm{V}_2$ ' then the relation between $V_1, V_2$ and $V_3$ is