Question

1. According to Bohr's theory, the radius of the $n^{th}$ orbit of an atom of atomic number $Z$ is proportional to

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

Answer 1

Answer: (C)

According to Bohr's theory, the coulomb force on the electron causes its centripetal acceleration.

$⟹\frac{1}{4\pi {ϵ}_0}\frac{Z{e}^2}{r^2}=\frac{m{v}^2}{r}$

Also one of Bohr's postulates states $mvr=\frac{nh}{2\pi }$

Thus eliminating $v$ from the equations gives

$⟹r\propto \frac{n^2}{Z}$