Question

Bohr radius for the hydrogen atom $(n=1)$ is approximately $0.530\mathring{A}$. The radius for the first excited state $(n=2)$ is (in $\mathring{A}$)

• A. 0.13
• B. 1.06
• C. 4.77
• D. 2.12

Answer 1

Answer: (D)

$r\propto n^2/Z$
where, $n=$ number of orbit
$Z=$ atomic number
$\because r_1\propto n_1^2$
$r_2\propto n_2^2$
( $Z=1$ for $H$-atom)
So $\frac{r_1}{r_2}=\frac{n_1^2}{n_2^2}$
$\frac{0.530}{r_2}=\frac{1^2}{2^2}$
$\therefore r_2=0.530\times 4=2.120\mathring{A}$