(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

The centripetal force for circular motion in the `n^(th)` orbit around the nucleus should be equal to the coulomb force
`:.(mv_(n)^(2))/(r_(n))=k((Ze)(e))/(r_(n)^(2))` where `k=9xx10^(9)Nm^(2)C^(-2)`
`:.(mr_(n)v_(n))v_(n)= ke^(2) [ :. "for" H_(2),Z=1]`
`:. (nh)/(2pi)v_(n)=ke^(2) [ :. mv_(n)r_(n)=(nh)/(2pi)]`
`:. v_(n)=(ke^(2)xx2pi)/(nh)`
`:.` Speed of electron in first orbit (n=1)
`v_(1)=(9xx10^(9)xx(1.6xx0^(-19))^(2)xx2.3.14)/((1)xx(6.625xx^(-34)))`
`=21.84xx10^(5)`
`:.v_(1)=2.184xx10^(6)m//s~~2.18xx10^(6)ms^(-1)`
`rArr` Spedd of electron in n =2 orbit,
`:.v_(n)=((ke^(2)xx 2pi)/(h))xx(1)/(n)=(v_(1))/(n)`
`:.v_(2)=(2.184xx10^(6))/(2)[ :. n=2]`
`:.v_(2)=1.092xx10^(6)m//s`