InterviewSolution
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InterviewSolution
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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`] |
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Answer» 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)` |
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