Question

If the attractive potential between electron and proton were given by $V\left(r\right)=V_{0}ln\left(\frac{r}{r_0}\right)$ (where $V_0,r_0$ are constants), the radius $r_n$ of the $nth$ Bohr orbit in Hydrogen atom would be proportional to

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

Answer 1

The correct option is B $n$

$V_{\left(r\right)}=V_{0}ln{\left(\frac{r}{r_0}\right)}_{nth}$

$r_n\alpha ?$

$r_n=$ radius of both orbit in H-atom

$F=-\frac{dv}{dr}=\frac{m{v}^2}{r}$

$v=\sqrt{\frac{Fr}{m}}$

and $m{v}_n{l}_n=\frac{nh}{2\pi }$ (angular momentum)

$ln2n$