Question

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

• A. Is proportional to $n^2$
• B. Is inversely proportional to $n^3$
• C. Has a constant value of $-7.2\text{eV}\mathring{A}$
• D. Has a constant value of $-10.2\text{eV}\mathring{A}$

Answer 1

The correct option is C Has a constant value of $-7.2\text{eV}\mathring{A}$

For Hydrogen like atoms,

$E_n=-13.6\frac{Z^2}{n^2}\text{eV};r_n=0.53\frac{n^2}{Z}\mathring{A}$

For hydrogen atom $Z=1$

$\Rightarrow E_n{r}_n=(-13.6\text{eV})\left(0.53\mathring{A}\right)$

$=-7.2\text{eV}\mathring{A}=\text{constant}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(C\right)$ is the correct answer.