Paragraph: The nuclear charge ( Ze ) is non-uniformly distributed within a nucleus of radius R . The charge density ρ ( r ) [charge per unit volume] is dependent only on the radial distance r from the

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Paragraph: The nuclear charge ( Ze ) is non-uniformly distributed within a nucleus of radius R . The charge density ρ ( r ) [charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. Question: For a = 0 , the value of d (maximum value of ρ as shown in the figure) is

TestHub · Accepted Answer

For a = 0 ​ ρ ( r ) = ( − R d ​ ⋅ r + d ) Now ∫ 0 R ​ ( 4 π r 2 ) ( d − R d ​ r ) d r = net charge = Z e ​ Solving this equation, we get d = π R 3 3 Z e ​

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