The ratio of ground state energy of $\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}$ is

If the longest wavelength of spectral line of Paschen series of $\mathrm{Li}^{2+}$ ion spectrum is $x \mathop {\rm{A}}\limits^{\rm{o}}$. Then the longest wavelength (in $\mathop {\rm{A}}\limits^{\rm{o}}$ ) of Lyman series of hydrogen spectrum is

If $v_0$ is the threshold frequency of a metal $X$, the correct relation between de-Broglie wavelength $(\lambda)$ associated with photoelectron and frequency $(v)$ of the incident radiation is

The difference in radii between fourth and third Bohr orbit of $\mathrm{He}^{+}($in m$)$ is