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Question

An electron orbiting around the nucleus of an atom

A
Has a magnetic dipole moment
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B
Exerts an electric force on the nucleus equal to that on it by the nucleus
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C
Does produce a magnetic induction at the nucleus
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D
Has a net energy, whose magnitude is inversely proportional to its distance from the nucleus.
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Solution

The correct option is D Has a net energy, whose magnitude is inversely proportional to its distance from the nucleus.
Given
r radius of atom
v velocity of electron

Magnetic moment
M=IA
Using
⎪ ⎪⎪ ⎪T=2πrvA=πr2I=qtI=ev2πr⎪ ⎪⎪ ⎪

M=ev2πr×πr2=evr2

From Bohr’s first postulates
mv2r=kZe2r2
mv22=kZe22r
Now mechanical energy
M.E.=mv22kZe2r
M.E.=kZe22rkZe2r=kZe22r
Net mechanical energy 1r

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