Search any question & find its solution
Question:
Answered & Verified by Expert
To calculate the size of a hydrogen anion using the Bohr model, we assume that its two electrons move in an orbit such that they are always on diametrically opposite sides of the nucleus. With each electron having the angular momentum $\hbar=\mathrm{h} / 2 \pi$, and taking electron interaction into account the radius of the orbit in terms of the Bohr radius of hydrogen atom $\mathrm{a}_{\mathrm{B}}=\frac{4 \pi \varepsilon_{0} \mathrm{~h}^{2}}{\mathrm{me}^{2}}$ is
Options:
Solution:
1831 Upvotes
Verified Answer
The correct answer is:
$\frac{4}{3} a_{B}$
$\begin{array}{l}
\mathrm{mvr}=\mathrm{n} \frac{\mathrm{h}}{2 \pi} \\
\& \frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{ke}^{2}}{\mathrm{r}^{2}}-\frac{\mathrm{ke}^{2}}{(2 \mathrm{r})^{2}} \\
\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{3}{4} \frac{\mathrm{ke}^{2}}{\mathrm{r}^{2}} \\
\Rightarrow \mathrm{mv}^{2} \mathrm{r}=\frac{3}{4} \mathrm{ke}^{2}
\end{array}$
Solving $(1)+(2)$
$\begin{array}{l}
\mathrm{r}=\frac{4 \pi \varepsilon_{0} \mathrm{~h}^{2}}{\mathrm{me}^{2}} \times \frac{4}{3} \\
\mathrm{r}=\frac{4}{3} \mathrm{a}_{\mathrm{B}}
\end{array}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.