Magnetic Moment and Principal Quantum No of electron

AI Thread Summary
The magnetic moment of a revolving electron around the nucleus is directly proportional to the principal quantum number, expressed as μ ∝ n. The relationship arises from the dependence of velocity and radius on the quantum number, where velocity varies inversely with n and radius varies with n squared. The correct equations indicate that while radius increases with n, velocity decreases, leading to the linear relationship for magnetic moment. The initial confusion stemmed from an incorrect assumption about the proportionality. Ultimately, the solution clarified that the magnetic moment is indeed proportional to the principal quantum number.
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Homework Statement


The magnetic moment of a revolving electron around the nucleus varies with principal quantum number as ?

Homework Equations


mvr = nh/2π

The Attempt at a Solution


i know μ = (qωr2 )/ 2

and after that i am substituting values for r and i get μ∝ n2 but that is wrong.Help !
 
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Welcome to PF;
How do you know it's wrong?

Doesn't v vary with n also?
 
Simon Bridge said:
Welcome to PF;
How do you know it's wrong?

Doesn't v vary with n also?

Well it was a MCQ ...the answer is μ ∝ n .

I got it though . Yup , v ∝ 1/n and r ∝ n2 . [ r = 0.529 n2 / Z Angstrom & v = 2.1 x 106 x Z / n m/s ]

Damn , this was an easy one , should have got it right in the first place ..!
 
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