Question

If in Bohr's atomic model, it is assumed that force between electron and proton varies inversely as $r^4$, energy of the system will be proportional to

• A. $n^2$
• B. $r^4$
• C. $n^6$
• D. $n^8$

Answer 1

Answer: (C)

$\frac{m{v}^2}{r}=\frac{k}{r^4}$
$V^2=\frac{k}{m{r}^3}$
$\text{ we know }$
$mvr=\frac{nh}{2x}$
$m^2{v}^2{r}^2=\frac{n^2{h}^2}{4{\pi }^2}$
$\frac{m^{2}kr}{mr}=\frac{n^2{h}^2}{4x^2}$
$r=\frac{m{k}^3{\pi }^2}{n^2{h}^2}$
$k\cdot f=\frac{1}{2}m{v}^2=\frac{1}{2}m/\frac{k}{m{r}^3}$
$=\frac{1}{2}{m}^m\frac{K}{m^1{m}^3}$
$E\alpha n^6$