Question

The radius of hydrogen atom in the ground state is $5.3\times {10}^{-11}\mathrm{m}$. After collision with an electron it is found to have a radius of $21.2\times {10}^{-11}\mathrm{m}$. The principal quantum number of the final state of the atom is

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is A

$2$

Explanation for the correct option:

(a) $2$

• Finding the atom's final state's fundamental quantum number.
• $\frac{{\mathrm{r}}_1}{{\mathrm{r}}_2}=\frac{{\mathrm{n}}_1^2}{{\mathrm{n}}_2^2}$
• It suggests that:
• $\frac{1}{{\mathrm{r}}_2}=\frac{5.3\times {10}^{-11}}{21.2\times {10}^{-11}}$
• It suggests that:
• $$\begin{gathered} {\mathrm{n}}_2^2=4 \\ {\mathrm{n}}_2=2 \end{gathered}$$
• Hence this option is correct

Hence the correct option is (a) $2$