Question

The radius of first orbit of hydrogen atom is $0.53A$. The radius of its fourth orbit will be-

• A. $0.193A$
• B. $4.24A$
• C. $2.12A$
• D. $8.48A$

Answer 1

The correct option is D $8.48A$

$\text{Given-}\ast \text{Radius of first orbit=0.53 A}$

$\text{We know that -}$

$\text{Radius of the orbit of}{e}^{-}\left(r\right),$

$\text{r}\alpha n^2,n\to n^{\text{th}}orbit$

$\Rightarrow \frac{r_1}{r_2}=\frac{n_1^2}{n_2^2}\text{Let}{r}_2\text{be the radius of}{4}^{\text{th}}\text{orbit}$

$\Rightarrow r_2=\frac{n_2^2}{n_1^2}\cdot r_1$

$\begin{array}{c}\text{for}{4}^{\text{th}}\text{orbit,}{n}_2=4\text{and}{n}_1=1\\ \Rightarrow r_2=(4{)}^2\cdot r_1=16\times 0.53A^{\circ }\\ \Rightarrow r_2=8.48A^{\circ }\\ \text{Hence, option (D) is correct.}\end{array}$