Question

According to Bohr's theory, which of the following correctly represents the variation of energy and radius of an electron in $n^{th}$ orbit of H-atom?

• A. $E_n\propto \frac{1}{n^2},r\propto \frac{1}{n^2}$
• B. $E_n\propto \frac{1}{n^2},r\propto n^2$
• C. $E_n\propto n^2,r\propto n^2$
• D. $E_n\propto n,r\propto \frac{1}{n}$

Answer 1

The correct option is B $E_n\propto \frac{1}{n^2},r\propto n^2$

According to Bohr's theory:
$r=\frac{n^2{h}^2}{4{\pi }^{2}mZ{e}^{2}k}$

$E_n=\frac{-k^{2}2{\pi }^{2}m{Z}^2{e}^4}{n^2{h}^2}$
So, option (b) is correct