Assume that protons and neutrons have equal m | vedclass

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(A) The density of a nucleus is given by $ho = \frac{	ext{Mass}}{	ext{Volume}}$.The mass of a nucleus with mass number $A$ is $M = A 	imes (1.6 \

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(A) The density of a nucleus is given by $ho = \frac{	ext{Mass}}{	ext{Volume}}$.The mass of a nucleus with mass number $A$ is $M = A 	imes (1.6 	imes 10^{-27} \ kg)$.The volume of a nucleus is $V = \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (1.5 	imes 10^{-15} A^{1/3})^3 = \frac{4}{3} \pi (1.5)^3 	imes 10^{-45} A \ m^3$.Calculating the nuclear density: $ho = \frac{1.6 	imes 10^{-27} A}{\frac{4}{3} 	imes 3.14 	imes 3.375 	imes 10^{-45} A} = \frac{1.6 	imes 10^{-27}}{14.137 	imes 10^{-45}} \approx 0.11317 	imes 10^{18} \ kg/m^3 = 1.1317 	imes 10^{17} \ kg/m^3$.The density of water is $ho_w = 10^3 \ kg/m^3$.The ratio is $\frac{ho}{ho_w} = \frac{1.1317 	imes 10^{17}}{10^3} = 1.1317 	imes 10^{14} = 11.317 	imes 10^{13}$.Comparing this with $n 	imes 10^{13}$,we get $n \approx 11$.

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