Question

The radius of the first Bohr orbit is

• A. $0.529\times {10}^{-10}m$
• B. $0.106\times {10}^{-10}m$
• C. $0.318\times {10}^{-10}m$
• D. None of these

Answer 1

Answer: (B)

$0.106\times {10}^{-10}m$

Given, $47.2eV$ is required to excite an electron from $n=2$ to $n=3$
$\Rightarrow \frac{13.6Z^2}{4}-\frac{13.6Z^2}{9}=\frac{5\times 13.6Z^2}{36}=47.2$

$\therefore Z^2=24.99$

Therefore, $Z=5$

Radius of first Bohr orbit is $=0.529\times \frac{1^2}{5}=0.1058\mathring{A}$

$\Rightarrow r_1=0.1058\times {10}^{-10}m$