Energy and radius of first Bohr orbit of He + and Li 2+ are [Given R H =2.18 × 10 -18 J , a 0 =52.9 pm ]

E n ( Li 2+ )=-19.62 × 10 -18 J ; r n ( Li 2+ )=17.6 pm E n ( He + )=-8.72 × 10 -18 J ; r n ( He + )=26.4 pm

E n ( Li 2+ )=-8.72 × 10 -18 J ; r n ( Li 2+ )=26.4 pm E n ( He + )=-19.62 × 10 -18 J ; r n ( He + )=17.6 pm

E n ( Li 2+ )=-19.62 × 10 -16 J ; r n ( Li 2+ )=17.6 pm E n ( He + )=-8.72 × 10 -16 J ; r n ( He + )=26.4 pm

E n ( Li 2+ )=-8.72 × 10 -16 J ; r n ( Li 2+ )=17.6 pm E n ( He + )=-19.62 × 10 -16 J ; r n ( He + )=17.6 pm

Chemistry · Structure of Atom

NEET (UG) 2025 — Question 46

Energy and radius of first Bohr orbit of $\mathrm{He}^{+}$ and $\mathrm{Li}^{2+}$ are

[Given $\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}, \mathrm{a}_{0}=52.9 \mathrm{pm}$ ]

Option A:
$\mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-19.62 \times 10^{-18} \mathrm{~J}$ ; $r_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm}$$\mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-8.72 \times 10^{-18} \mathrm{~J}$ ; $\mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm}$
Correct
Option B:
$\mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-18} \mathrm{~J}$ ; $r_{n}\left(\mathrm{Li}^{2+}\right)=26.4 \mathrm{pm}$$\mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-18} \mathrm{~J}$ ; $\mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm}$
Option C:
$\mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-19.62 \times 10^{-16} \mathrm{~J}$ ; $r_{n}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm}$$\mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-8.72 \times 10^{-16} \mathrm{~J} ;$$\mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm}$
Option D:
$\mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-16} \mathrm{~J}$ ; $r_{n}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm}$$\mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-16} \mathrm{~J}$ ; $\mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm}$

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

For $\mathrm{He}^{+} \Rightarrow \mathrm{E}_{1}=-2.18 \times 10^{-18} \times \frac{2^{2}}{1^{2}} \mathrm{~J}$

=-8.72 \times 10^{-18} \mathrm{~J}

For $\mathrm{Li}^{2+} \Rightarrow \mathrm{E}_{1}=-2.18 \times 10^{-18} \times \frac{3^{2}}{1^{2}} \mathrm{~J}$

=-19.62 \times 10^{-18} \mathrm{~J}

$r_{n}=52.9 \times \frac{n^{2}}{Z} p m$

For $\mathrm{He}^{+} \Rightarrow \mathrm{r}_{1}=52.9 \times \frac{1^{2}}{2} \mathrm{pm}=26.4 \mathrm{pm}$

For $\mathrm{Li}^{2+} \Rightarrow \mathrm{r}_{1}=52.9 \times \frac{1^{2}}{3} \mathrm{pm}=17.6 \mathrm{pm}$

Answer key and solution verified before publishing.

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