Answer
$T=n^3T_1$ $n=1,2,3,....$
where $T_1=\frac{h^3}{4\pi^2mk^2e^4}$
Work Step by Step
We know that
$T=\frac{2\pi r_n}{v_n}$
but $r_n=\frac{n^2h^2}{4\pi^2mke^2}$
and $v_n=\frac{2\pi ke^2}{nh}$
Now $T=\frac{2\pi(\frac{n^2h^2}{4\pi^2mke^2})}{\frac{2\pi ke^2}{nh}}$
This simplifies to:
$T=n^3(\frac{h^3}{4\pi^2mk^2e^4})$
$T=n^3T_1$ $n=1,2,3,....$
where $T_1=\frac{h^3}{4\pi^2mk^2e^4}$
