(a) Using the Bohr's model, calculate the speed of the electron in a hydrogen atom in the n=1,2 and 3 levels. (b) Calculate the orbital period in each of these levels.

Explanation

(a) form `v=c/n alpha`, where `alpha=(2piKe^2)/(ch)=0.0073`
`v_1=(3xx10^8)/1xx0.0073=2.19xx10^6m//s, v_2=(3xx10^8)/2xx0.0073=1.095xx10^6m//s`
`v_3=(3xx10^8)/3xx0.0073=7.3xx10^5m//s`.
(b) Orbital period, `T=(2pir)/v. As r_1=0.53xx10^(-10)m, T_1=(2pixx0.53xx10^(-10))/(2.19xx10^6)=1.52xx10^(-16)s`
As `r_2=4r_1 and v_2=1/2v_1`
`T_2=8T_1=8xx1.52xx10^(-16)s=1.216xx10^(-15)s`
As `r_3=9r_1 and v_3=1/2v_1`
`:. T_3=27T_1=27xx1.52xx10^(-16)s=4.1xx10^(-15)s`