(3)

$E_n=-2.18\times {10}^{-18}\frac{Z^2}{n^2}\text{J}$

For first Bohr orbit of $H{e}^{+}$,

$E_{{\text{He}}^{+}}=-2.18\times {10}^{-18}\times \frac{4}{1}=-8.72\times {10}^{-18}\text{J}$

For first Bohr orbit of $L{i}^{2+}$,

$E_{{\text{Li}}^{2+}}=-2.18\times {10}^{-18}\times \frac{9}{1}=-19.62\times {10}^{-18}\text{J}$

Bohr’s radius, $r_n=52.9\times \frac{n^2}{Z}\text{pm}$

For first Bohr orbit of $H{e}^{+}$,

$r_{\left({\text{He}}^{+}\right)}=52.9\times \frac{1}{2}=26.45$ $\mathrm{pm}$

For first Bohr orbit of $L{i}^{2+}$,

$r_{\left({\text{Li}}^{2+}\right)}=52.9\times \frac{1}{3}=17.63$ $\mathrm{pm}$

(1)

$E_n=-R_H\frac{Z^2}{n^2}$

For ground state $H{e}^{+}$ ion, Z = 2, n = 1,

        $E_1=-R_H\frac{2^2}{1^2}=-4R_H=-x\text{ J}$

For an electron in n = 2 state for $B{e}^{3+}$ ion (Z = 4),

        $E_2=-R_H\frac{4^2}{2^2}=-4R_H=-x\text{ J}$

(1)

Radius $=r_0\times \frac{n^2}{Z}$

For $H{e}^{+},n=2,Z=2$

$r_{{\text{He}}^{+}}=r_0\times \frac{2\times 2}{2} ; 105.8=r_0\times 2$

$r_0=\frac{105.8}{2}\text{pm}$

For $L{i}^{2+} ;n=3,Z=3$

$r_{{\text{Li}}^{2+}}=r_0\times \frac{{\left(3\right)}^2}{3}=\frac{105.8}{2}\times 3=158.7\text{ pm or }1.587$ $\mathrm{\AA }$