
Given
Radius of orbit = r = 0.5 Å = 0.5 X 10-10 m
Frequency of revolution =
f =
1010 MHz = 1016
Hz
Charge on electron = e = 1.6 X 10 -19 C
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 r2
_ _ _ _ _ _ _ _ _
_ (3)
From equation (1) (2) and
(3) we get
M
= e f π r2
M
= 1.6 X 10 -19 X 1016 X 3.14 X (0.5 X 10-10 )2
M
= 1.6 X 10 -19 X 1016 X 3.14 X 0.25 X 10-20
M
= 1.6 X 3.14 X 0.25 X 10 -19 X 1016 X 10-20
M = 1.256 X 10 -23 Am2
The equivalent magnetic
moment of an electron revolving around a nucleus in an orbit of radius 0.5 Å
with frequency 1010MHz is 1.256
X 10 -23 Am2
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