Question

According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of an atom of atomic number Z is proportional to

• A. $\frac{Z^2}{n^2}$
• B. $\frac{Z^2}{n}$
• C. $\frac{Z}{n}$
• D. $Z^2{n}^2$

Answer 1

The correct option is A $\frac{Z^2}{n^2}$

According to Bohr's theory, $E_n=\left(\frac{-m{e}^4}{8{ϵ}_0^2{h}^2}\right)\frac{Z^2}{n^2}=\frac{C{Z}^2}{n^2}$ where $C$ is a constant.
Hence, $E_n\propto \frac{Z^2}{n^2}$ and the correct choice is (a).