1.

(2) An electron in an atom revolves around thenucleus in an orbit of radius 0.5A. Calculate the(Cequivalent magnetic moment, if the frequency ofrevolution of electron is 1010 MHz(Ans : 1.257 × 10"23 Am")

Answer»

Given

Radius of orbit = r= 0.5 Å = 0.5 X 10^-10m

Frequency of revolution = f = 10^10MHz = 10^16Hz

Charge on electron = e = 1.6 X 10^-19C

Magnetic moment = M = ?

The electron revolving in a circular orbit around the nucleus behaves as a current loop and hence posses a magnetic momentum

The magnetic momentum can be given as

M = I A

_ _ _ _ _ _ _ _ _ _ (1)

Where

I is a current flowing through the circular loop

i.e.

I = e / T

T is a time period=1 / f

Therefore

1 / T = f

I = e f

_ _ _ _ _ _ _ _ _ _ (2)

And

A is a area of circular loop

i.e.

A = π r^2

_ _ _ _ _ _ _ _ _ _ (3)

From equation (1) (2) and (3) we get

M = e f π r^2

M = 1.6 X 10^-19X 10^16X 3.14 X (0.5 X 10^-10)^2 M = 1.6 X 10^-19X 10^16X 3.14 X 0.25 X 10^-20 M = 1.6 X 3.14 X 0.25 X 10^-19X 10^16X 10^-20 M = 1.256 X 10^-23Am^2

The equivalent magnetic moment of an electron revolving around a nucleus in an orbit of radius 0.5 Å with frequency 10^10MHz is1.256 X 10^-23Am^2

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