Calculate the velocity of an electron present in third orbit of H atom. Also calculate number of revolutions per second round the nucleus.

Explanation

Velocity of electron is given as :
`v = (2 pi e^2)/(nh)`
Now, `e= 4.8 xx 10^(-10) e.s.u. , n = 3, h = 6.63 xx 10^(-27)` erg sec
`:. v = (2 xx 22 xx (4.8 xx 10^(-10))^(2))/(7 xx 3 xx 6.63 xx 10^(-27))`
`= 7.27 xx 10^7 cm s^(-1)`
No. of revolutions per second = `("Velocity")/("Circumference")`
`= v/(2pi r)`
but `r = (4 pi^2 m e^2)/(n^2 h^2)`
`:.` No. of revolutions = `(2 pi e^2)/(nh) xx (4 pi^2 m e^2)/(2 pi n^2 h^2)`
`= (4 pi^2 m e^4)/(n^3 h^3)`
` = (4 xx (22/7)^2 xx (9.1 xx 10^(-28)) xx (4.8 xx 10^(-10))^4)/(3^3 xx (6.626 xx 10^(-24))^3)`
`= 2.42 xx 10^(14)`