Question

Calculate the velocity of an electron placed in the `3^(rd)` orbit of the `Li^(2+)` ion. Also calculate the number of revolution per second that it makes around the nucleous.

Answer 1

Radius of `2^(nd)` orbit `= r_(1) xx ((n)^(2))/(Z)=0.529xx10^(-8) xx ((3)^(2))/(3) = 1.587 xx 10^(-8)cm`
Velocity of electron in `2^(nd)` orbit,
`v=2//18xx10^(8)(Z)/(n)cm//sec = (2.18xx10^(8)xx3)/(3) = 2.18xx10^(8)cm//sec`
No. of revolution/sec `= (1)/(2pir//v)=(v)/(2pir) = (2.18xx10^(8)cm//sec)/(2xx3.14xx1.587xx10^(-8)cm)`
`= 0.2187 xx 10^(16) = 2.187 xx 10^(15) "rev/sec"`