Determine the ratios of time periods of an electron in Bohr orbits of a hydrogen atom.

Explanation

Time period,
`T_n=("circumference of the orbit")/("velocity of electron") =(2pi r_n)/(v_n)`
If the principal quantum number be n(-1,2,3,….) then,
`r_n prop n^2 and v_n prop 1/n`
so, `T_n prop n_3, i.e., T_1:T_2:T_3:….. =1:8:27:……`