The radius R of a nucleus of mass number A ca | vedclass

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Question

(C) The mass of a nucleus is approximately $M = A 	imes M_{	ext{nucleon}}$,where $M_{	ext{nucleon}} \cong 1.67 	imes 10^{-27} \; kg$.The volume of

Vedclass · Accepted Answer

$10^{17} \; kg \; m^{-3}$

Vedclass · Answer

(C) The mass of a nucleus is approximately $M = A 	imes M_{	ext{nucleon}}$,where $M_{	ext{nucleon}} \cong 1.67 	imes 10^{-27} \; kg$.The volume of the nucleus is $V = \frac{4}{3} \pi R^3$.Substituting $R = R_0 A^{1/3}$ where $R_0 = 1.3 	imes 10^{-15} \; m$,we get $V = \frac{4}{3} \pi (R_0 A^{1/3})^3 = \frac{4}{3} \pi R_0^3 A$.The density $ho$ is given by $ho = \frac{M}{V} = \frac{A 	imes M_{	ext{nucleon}}}{\frac{4}{3} \pi R_0^3 A} = \frac{M_{	ext{nucleon}}}{\frac{4}{3} \pi R_0^3}$.Substituting the values: $ho = \frac{1.67 	imes 10^{-27}}{\frac{4}{3} 	imes 3.14 	imes (1.3 	imes 10^{-15})^3} \cong \frac{1.67 	imes 10^{-27}}{4.186 	imes 2.197 	imes 10^{-45}} \cong 1.8 	imes 10^{17} \; kg \; m^{-3}$.Thus,the order of magnitude is $10^{17} \; kg \; m^{-3}$.

The radius $R$ of a nucleus of mass number $A$ can be estimated by the formula $R = (1.3 \times 10^{-15}) A^{1/3} \; m$. It follows that the mass density of a nucleus is of the order of $(M_{\text{prot}} \cong M_{\text{neut}} = 1.67 \times 10^{-27} \; kg)$.

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