Question

According to Bohr's theory of hydrogen atom, the product of the binding energy of the electron in $n^{th}$ orbit and the radius of the $n^{th}$ orbit :

• A. is proportional to $n^2$
• B. is inversely proportional to $n^3$
• C. has a constant value of $10.2eV{A}^0$
• D. has a constant value of $7.2eV{A}^0$

Answer 1

The correct option is A is proportional to $n^2$

$En\propto \frac{1}{n^2}$ & $r_n\propto n^2$

$\therefore$ $E_n{r}_n$ is independent of $n$. Hence, $E_1{r}_1=\left(13.6eV\right)\left(0.53\stackrel{o}{A}\right)=7.2eV\stackrel{o}{A}$