Question

The radius of hydrogen atom in its ground state is $ 5.3 \times 10^{-11}\, m $ . After collision with an electron it is found to have a radius of $ 21 .2 \times 10^{-11}\, m $ . What is the principal quantum number $ n $ of the final state of atom 7

• A. $ n = 4 $
• B. $ n = 2 $
• C. $ n = 16 $
• D. $ n = 3 $

Answer 1

Answer: (B)

$r \propto n^{2}$
ie, $\frac{r_{f}}{r_{i}}=\left(\frac{n_{f}}{n_{i}}\right)^{2}$
$\Rightarrow \frac{21.2 \times 10^{-11}}{5.3 \times 10^{-11}}=\left[\frac{n}{1}\right]^{2}$
$\Rightarrow n^{2}=4$
$\Rightarrow n=2$