Find the velocity of electron revolving in the third orbit of hydrogen atom. Also determine the number of revolutions of the electron per second around the nucleus.

Explanation

The velocity of the electron revolving in the 3rd orbit around the nucleus of hydrogen atom.
`v_(3)=(2pie^(2))/(3xxh)=(2xx3.14xx(4.8xx10^(-10))^(2))/(3xx(6.627xx10^(-27)))=7.278xx10^(7)cm*s^(-1)`
Radius of the 'n' th orbit of H-atom, `r_(n)=(n^(2)h^(2))/(4pi^(2)me^(2))`
`therefore`Radius of the third orbit `(r_(3))=(3^(2)h^(2))/(4pi^(2)me^(2))`
`=(9xx(6.627xx10^(-27))^(2))/(4xx(3.14)^(2)xx(9.108xx10^(-28))xx(4.8xx10^(-10))^(2))`
`=4.77xx10^(-8)cm" "[m=9.108xx10^(-28)g]`
Circumference of the third orbit
`=2pir_(3)=2xx3.14xx4.77xx10^(-8)=2.99xx10^(-7)cm`
`therefore`Number of revolutions of electron per second around the
nucleus`=("Velocity")/("Circumference of the orbit")`
`=(7.278xx10^(7))/(2.99xx10^(-7))=2.43xx10^(14)`