Q24 / 150 · MHT CET 2024 (10 May Shift 1) · Chemistry

Which of the following is radius of first orbit of $\mathrm{He}^{+}$?

  • A
    52.90 pm
  • B
    78.90 pm
  • Correct answer
    C
    26.45 pm
  • D
    13.35 pm

Solution

Radius of $\mathrm{n}^{\text {th }}$ orbit $=\mathrm{r}_{\mathrm{n}}=\frac{52.9 \times(\mathrm{n})^2}{\mathrm{Z}} \mathrm{pm}$ $\mathrm{He}^{+}$is a hydrogen-like species having $\mathrm{Z}=2$. Radius of the first orbit of $\mathrm{He}^{+}$ $\begin{aligned} & =\mathrm{r}_1 \\ & =\frac{52.9 \times(1)^2}{2} \mathrm{pm} \\ & =26.45 \mathrm{pm} \end{aligned}$

Hence, the correct answer is option: 'C'.

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