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

The difference in radii between fourth and third Bohr orbits of $\mathrm{He}^{+}$(in m) is
  1. $2.64 \times 10^{-10}$
  2. $1.85 \times 10^{-12}$
  3. $1.85 \times 10^{-10}$
  4. $1.85 \times 10^{-9}$

Solution

Bohr radii $\left(\mathrm{r}_{\mathrm{n}}\right)=52.9 \times \frac{\mathrm{n}^2}{\mathrm{Z}} \mathrm{pm}$ radii of fourth orbit of $\mathrm{He}^{+}=52.9 \times \frac{(4)^2}{2}$
radii of third orbit of $\mathrm{He}^{+}=52.9 \times \frac{(3)^2}{2}$
difference of radii $=52.9 \times \frac{(4)^2}{2}-52.9 \times \frac{(3)^2}{2}$ $\begin{aligned} & =\frac{52.9}{2} \times 7 \mathrm{pm} \\ & =185.15 \mathrm{pm} \\ & =185.15 \times 10^{-12} \mathrm{~m} \\ & =1.85 \times 10^{-10} \mathrm{~m} \end{aligned}$

Asked in: AP EAMCET 2024 (21 May Shift 2)

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