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 $\frac{r_{1}}{r_{2}}=\frac{n_{1}^{2}}{n_{2}^{2}}$
$\frac{0.530}{r_{2}}=\frac{1^{2}}{2^{2}}$
$\therefore r_{2}=0.530 \times 4=2.120\, \mathring{A}$