Question
Time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is
A.
$$\frac{{4{\pi ^2}m{r^2}}}{{nh}}$$
B.
$$\frac{{nh}}{{4{\pi ^2}mr}}$$
C.
$$\frac{{2\pi mr}}{{{n^2}{h^2}}}$$
D.
$$\frac{h}{{2\pi mr}}$$
Answer :
$$\frac{{4{\pi ^2}m{r^2}}}{{nh}}$$
Solution :
$${\text{Angular momentum}}$$ $$ = m\nu r = \frac{{nh}}{{2\pi }};\nu = \frac{{nh}}{{2\pi mr}}$$
$$\eqalign{
& {\text{As, Time period}} = \frac{{{\text{Circumference}}}}{{{\text{Velocity}}}} \cr
& T = \frac{{2\pi r}}{\nu } = \frac{{2\pi r}}{{\frac{{nh}}{{2\pi mr}}}} = \frac{{4{\pi ^2}m{r^2}}}{{nh}} \cr} $$