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Old Sep 24th 2009, 09:19 AM   #1
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help genii

1.According to Bohr model, magnetic field at the centre (at the nucleus) of a hydrogen atom due to the motion of electron in nth orbit is proportional to which given option
(A) 1/n3 (B) 1/n5 (C) n5 (D) n3

plz explain also. i dont know to solve it.. I wonder magnetic field means intensity or its momenton or strength.. Despite these also i have no idea.
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Old Sep 25th 2009, 11:22 PM   #2
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This is an interesting question.

Think of the Hydrogen atom with the nucleus at the centre.

Think of the orbit as a circular wire around it.

The Bohr quantization condition gives us the angular momentum L

$\displaystyle L\ =\ m\ \omega\ r^2\ =\ \frac{n\ h}{2\ \pi}$ .

Thus it can be seen that omega is proportional to n . But

$\displaystyle \omega\ =\ 2\ \pi \ f$ where f is the frequency.

So f is proportional to n

Thus, if we look at any point on the "orbit wire" , it is as though f electrons pass it each sec ( actually it is the same one !)

Thus a charge of f . e coulombs passes any point on the wire per sec.

e here is the charge of the electron.

This corresponds to a current of $\displaystyle I\ =\ \frac{f\ e}{1}$ .

Thus I is also proportional to n.

Now look up the formula for the magnetic field at the centre of a current carrying loop and find what power of I it corresponds to.

It should be the same for n.
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