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 $10.2\, eV -\mathring{A}$
• D. has a constant value of $7.2\, eV -\mathring{A}$

Answer 1

Answer: (D)

$E_{n} \propto \frac{1}{n^{2}}$ and $r_{n} \propto n^{2}$
Therefore, $E_{n} r_{n}$ is independent of $n$.
Hence, $E_{1} r_{1}=(13.6\, eV )(0.53 \,\mathring{A})$
$=7.2 \,cV -\,\mathring{A}=$ constant