An electron in an atom revolves around the nucleus in an orbit of radius 0.53 angstrom. Calculate the equivalent magnetic moment if the frequency of revolution of electron is 6.8 x 10 9 MHz.
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The equivalent magnetic moment is 9.6 x 10∧ -24 Am².
Given: radius of orbit = r =0.53 angstrom.
charge of electron = q = e = 1.6 x 10 ∧-19
Frequency of revolution of electron= f = 6.8 x 10∧9MHz.
= 6.8 x 10∧15 Hz.
To Find: Equivalent magnetic moment= ?
Solution :
We know the equation for magnetic moment : M=NIA
Where, N= No. of turns =1
I= current
A= area = πr²
We know charge (q) = current (I)/Time (t)
So I = t x q
f = 1/t
So I = f x q
Putting values in the equation, M=NIA
M= N x f x q x π x r²
=1 x 6.8 x 10∧15 x 1.6 x 10 ∧-19 x 3.14 x (0.53 x 10 ∧-10)²
= 9.6 x 10∧ -24 Am².
Therefore, the equivalent magnetic moment is 9.6 x 10∧ -24 Am².