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Question

# An atom is modelled as a point charge of +e at the nucleus with the electron charge distribution, described by the charge densityρ=−15e8πa3(1−r2a2) for r≤a<0ρ≃0 for r>a, where 'a' is a constant.The net charge contained within a sphere of radius r < a is :

A
[3r52a54r43a4]e
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B
[3r52a55r32a3]e
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C
[3r52a55r32a3+1]e
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D
Zero
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Solution

## The correct option is D [3r52a5−5r32a3+1]eNet charge within the sphere of radius r≤ae+∫r0(4πr2dr)ρ=e+4π(−15e8πa3)∫r0(1−r2a2)r2dr=e(1+3r52a5−5r32a3)

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