Question

The radius of second orbit in an atom of hydrogen is R. What is the radius in third orbit.

• A. $3R$
• B. $2.25R$
• C. $9R$
• D. $\frac{R}{3}$

Answer 1

The correct option is B $2.25R$

$r_n=0.529\frac{n^2}{Z}\stackrel{o}{A}$ where $r_n$ is radius of $n^{th}$ orbit.

$n=$ number of the orbit.

$Z=$ atomic number.

Given:

$Z=1$ (Hydrogen orbit)

$R=0.529\times \frac{(2{)}^2}{1}=4\times 0.529$

Now let radius of $3^{th}$ orbit be x.

$x=0.529\frac{n^2}{Z}\stackrel{o}{A}=0.529\frac{(3{)}^2}{Z}\stackrel{o}{A}=0.529\times \frac{9}{1}\stackrel{o}{A}=0.529\times \frac{4}{4}\times \frac{9}{1}\stackrel{o}{A}=R\times \frac{9}{4}=2.25R$

Hence the correct option is (B).