Question

An electron is revolving in the $n^{th}$ orbit of radius $4.2 ?$, then the value of $n$ is $(r_1 = 0.529 ? )$

• A. $4$
• B. $5$
• C. $6$
• D. $3$

Answer 1

Answer: (D)

$3$

Answer 2

Since $r_{n}\propto n^{2}, \frac{r_{n}}{r_{1} } = \frac{n^{2}}{\left(1\right)^{2}}$ $\therefore r_{n} =n^{2}r_{1}$ or $n^{2} = \frac{r_{n}}{r_{1}}$ $\Rightarrow n= \sqrt{\frac{r_{n}}{r_{1}}}$ $= \sqrt{\frac{4.2}{0.529}}$ $= \sqrt{7.939}$ $= 2.81 \approx 3.$