The electron in a hydrogen atom make a transtion $n_1\to n_2$ where $n_1\text{and}{n}_2$ are the priocipal quantum number of the two states . Assume the Bohr model to be valid . The time period of the electron in the initial state is eight time that in the state . THe possible values of $n_1\text{and}{n}_2$ are

Answer: A::DSolution: The time period of the electron in a bohr is given
by $T=\frac{2\pi r}{\nu }$
Since the for the bohr orbit , $m\nu r=n\left(h/2\pi \right)$ , the time period because
$T=\frac{2\pi r}{nh/\left(2\tau mr\right)}=\left(\frac{4{\pi }^{2}m}{nh}\right)$
since the radius of the orbit r depends on n, we replace r bohr radius of a hydrogen atom is
$r=n^2(\frac{h^2{ϵ}_0}{\tau m{e}^2}$
Hence , T = ((4 pi ^(2) m)/(nh)) (( n^(2) h^(4) epsilon_(0)^(2))/(pi ^(2) m^(2) e^(4))) = n^(2) (( 4h^(3) epsilon_(0)^(2))/(me^(4)))for two orbit $T_1\frac{)}{T_2}={\left(\frac{n_1}{n_2}\right)}^2$
it is given that $T_1/T_2=8,$ heanse $n_1/n_2=2$