Question

The electric potential between a proton and an electron is r given by $V = V_0 in\frac{r}{r_0}, where r_0$ is a constant. Assuming Bohr's model to be applicable, write variation of rn with n, n being the principal quantum number.

• A. $r_n?n$
• B. $r_n?\frac{1}{n}$
• C. $r_n?n^2$
• D. $r_n?\frac{1}{n^2}$

Answer 1

Answer: (A)

$r_n?n$

Answer 2

$U=eV=eV_0 in\bigg(\frac{r}{r_0}\bigg)$ $|F|=\bigg|-\frac{dU}{dr}\bigg|=\frac{eV_0}{r}$ This force will provide the necessary centripetal force. Hence, $\frac{mv^2}{r}=\frac{eV_0}{r}$ or $v=\sqrt{\frac{eV_0}{m}}$...(i) Moreover, $mvr=\frac{nh}{2\pi}$...(ii) Dividing E (ii) by (i), we have or $r_n?n$