Question

An electron in an atom revolves around the nucleus in an orbit of radius 0.53 Å. If the frequency of revoluation of an electron is `9xx10^(9)` MHz. calculate the orbital angular momentum.
[Given : Charge on an electron `=1.6xx10^(-19)C`, Gyromagnetic ratio `8.8xx10^(10)C//kg, pi =3.142`]

Answer 1

Given, `r=0.53 Å=0.53xx10^(-10)m.`
`f=9xx10^(9)MHz=9xx10^(15)Hz.`
Gyromagnetic ratio
`=8.8xx10^(10)C//kg`
Now, Period,
`T=(1)/(f)=(1)/(9xx10^(15))`
Current `(I)=(e )/(T)=ef`
The electron revolving in the circular orbit behaves as a current loop and hence possesses magnetic moment.
Magnetic Moment (M)
`=IA=ef xx pi r^(2)`
`therefore M=1.6 xx 10^(-19)xx9xx10^(15)x3.142xx(0.53xx10^(-10))^(2)`
`M=12.709xx10^(-24)Am^(2)`
Angular momentum (L)
`=("Magnetic Moment (M)")/("Gyromagnetic Ratio")`
`=(12.709xx10^(-24))/(8.8xx10^(10))`
`=1.444 xx 10^(-34)kg m^(2)s^(-1)`