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Question : 7
Total: 8
A electron of mass m e + Z e
=
Solution:
(i) Behaviour of revolving electron as a tiny magnetic dipole
(ii) Proof of the relation
= −
(iii) Significance of negative sign
Electron, in circular motion around the nucleus, constitutes a current loop which behaves like a magnetic dipole.
Current associated with the revolving electron :
I =
and T =
∴ I =
v
Magnetic moment of the loop,µ = I A
µ = L A =
π r 2 =
=
Orbital angular momentum of the electron
L = m e v r
=
-ve sign signifies that the angular momentum of the revolving electron is opposite in direction to the magnetic moment associated with it.
(ii) Proof of the relation
(iii) Significance of negative sign
Electron, in circular motion around the nucleus, constitutes a current loop which behaves like a magnetic dipole.
Current associated with the revolving electron :
Magnetic moment of the loop,
Orbital angular momentum of the electron
-ve sign signifies that the angular momentum of the revolving electron is opposite in direction to the magnetic moment associated with it.
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