Question

If the average life time of an excited state of hydrogen is of the order of ${10}^{-8}s$, estimate how many orbits an electron makes when it is in the state $n=2$ before it suffers a transition to state $n=2$(Bohr radius $a_0=5.3\times {10}^{-11}m)$ ?

Answer 1

The velocity of $e^{-}$ in $2nd$ orbit of $H^{-}$ atom,
$U=1.09\times {10}^{8}cm/s$
The orbit frequency to be
$\frac{Velocityof{e}^{-}}{2\pi r_3}=\frac{\mu }{2x{r}_2}$
$t=\frac{1.09\times {10}^8}{2\times 3.14\times 0.529\times {10}^{-8}\times 4}$
$t=8.2\times {10}^{14}/8$
The number of orbits made by the
$=8.2\times {10}^{14}/8\times {10}^{-8}$
$8\times {10}^6$