Question

Suppose the potential energy between an electron and a proton at a distance $r$ is given by $\frac{K{e}^2}{3r^3}$. Application of Bohr's theory to hydrogen atom in this case shows that

• A. Energy in the $n^{th}$ orbit is proportional to $n^{-6}$
• B. Energy is proportional to $m^{-3}$ ($m$ = mass of electron)
• C. Energy in the $n^{th}$ orbit is proportional to $n^{-2}$
• D. Energy is proportional to $m^3$ ($m$ = mass of electron)

Answer 1

Answer: (A), (B)

The correct options are
A Energy in the $n^{th}$ orbit is proportional to $n^{-6}$
B Energy is proportional to $m^{-3}$ ($m$ = mass of electron)

Bohr's Theory $r=90\frac{n^2}{z}$ i.e. $r\propto n^2$

given that $E\propto \frac{1}{r^3}$ & $r\propto n^2$

so$E\propto \frac{1}{n^6}$

$r=\frac{n^2{h}^2}{4{\pi }^{2}mkZ{e}^2}$

i.e $r\propto \frac{1}{m}$

$\Rightarrow E\propto \frac{1}{m^3}$

as $E\propto \frac{1}{r^3}$

$E\propto m^{-3}$