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Question: Answered & Verified by Expert
Calculate radius of third orbit of $\mathrm{He}^{+}$.
ChemistryStructure of AtomMHT CETMHT CET 2023 (14 May Shift 1)
Options:
  • A $52.9 \mathrm{pm}$
  • B $105.8 \mathrm{pm}$
  • C $238.1 \mathrm{pm}$
  • D $423.2 \mathrm{pm}$
Solution:
1112 Upvotes Verified Answer
The correct answer is: $238.1 \mathrm{pm}$
$$
\mathrm{r}_{\mathrm{n}}=\frac{52.9(\mathrm{n})^2}{\mathrm{Z}} \mathrm{pm}
$$
$\mathrm{He}^{+}$is a hydrogen-like species having $\mathrm{Z}=2$. Radius of the third orbit of $\mathrm{He}^{+}$
$=\mathrm{r}_3=\frac{52.9 \times(3)^2}{2} \mathrm{pm}=238.1 \mathrm{pm}$

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