Magnetic Moment and Principal Quantum No of electron

In summary, the magnetic moment of a revolving electron around the nucleus varies with principal quantum number as μ ∝ n, with v ∝ 1/n and r ∝ n^2. This was determined through the equation mvr = nh/2π and the knowledge that μ = (qωr^2)/2. The correct answer for this MCQ was μ ∝ n.
  • #1
TheOtherPlace
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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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  • #2
Welcome to PF;
How do you know it's wrong?

Doesn't v vary with n also?
 
  • #3
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 ..!
 

FAQ: Magnetic Moment and Principal Quantum No of electron

What is a magnetic moment?

A magnetic moment is a measure of the strength and direction of a magnetic field produced by a moving electric charge, such as an electron.

How is magnetic moment related to principal quantum number?

The magnetic moment of an electron is directly proportional to its principal quantum number. As the principal quantum number increases, the magnetic moment also increases.

Why is the magnetic moment important in quantum mechanics?

In quantum mechanics, the magnetic moment of an electron plays a crucial role in determining the energy levels and behavior of atoms and molecules. It is also important in understanding phenomena such as spin and orbital angular momentum.

How is the magnetic moment of an electron calculated?

The magnetic moment of an electron can be calculated using the equation μ = √(s(s+1)ħ²), where μ is the magnetic moment, s is the spin quantum number, and ħ is the reduced Planck constant.

What is the significance of the principal quantum number in determining the magnetic properties of an atom?

The principal quantum number, along with the spin quantum number, determines the energy level and orientation of an electron, which in turn affects its magnetic properties. Higher principal quantum numbers result in higher magnetic moments and stronger magnetic fields.

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