Question

The radius of the electron's second stationary orbit in Bohr's atom, is $R$. The radius of the third orbit will be,

• A. $3R$
• B. $2.25R$
• C. $0.25R$
• D. $\frac{R}{3}$

Answer 1

The correct option is B $2.25R$

Radius of an electron in $n^{th}$ Bohr's orbit is given as,
$r_n=\frac{r_1{n}^2}{Z}\text{in}\mathring{\text{A}}\Rightarrow r_n\propto n^2$

Let $r_2$ and $r_3$ be the radii of second and third orbits, then,

$\frac{r_2}{r_3}={\left(\frac{n_2}{n_3}\right)}^2$
$\Rightarrow \frac{R}{r_3}={\left(\frac{2}{3}\right)}^2$
$\therefore r_3=\frac{9R}{4}=2.25R$

Hence, $\left(B\right)$ is the correct answer.

Why this question ? It clears the concept of radius of nth orbit of Bohr's hydrogen atom.