Question

Suppose that the potential energy of a hypothetical atom consisting of a proton and an electron is given by U = - Ke${}^2$ / 3 r${}^3$.Then if Bhor's postulates are applied to this atom ,then the radius of the n ${}^{th}$ orbit will be proportional to:

• A. n${}^2$
• B. 1 / n${}^2$
• C. n${}^3$
• D. 1 / n${}^3$

Answer 1

The correct option is A n${}^2$

$u=\frac{-k{e}^2}{2r^3}$

$F=\frac{-du}{dr}$

$=\frac{k{e}^2}{r^2}$

$\frac{k{e}^2}{r^2}=\frac{m{v}^2}{r}$---------------$\left(1\right)$

$mvr=\frac{nh}{2\pi }$---------------$\left(2\right)$

$\Rightarrow r\alpha n^2$

Hence,

option $\left(A\right)$ is correct answer.