The radius of a nucleus with mass number A is | vedclass

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(D) The radius of the nucleus is given by $R_{n} = 1.25 	imes 10^{-13} 	imes A^{1/3} \ cm$. For $A = 64$,$R_{n} = 1.25 	imes 10^{-13} 	imes (64)^{

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$1.25 	imes 10^{-13}$

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(D) The radius of the nucleus is given by $R_{n} = 1.25 	imes 10^{-13} 	imes A^{1/3} \ cm$. For $A = 64$,$R_{n} = 1.25 	imes 10^{-13} 	imes (64)^{1/3} = 1.25 	imes 10^{-13} 	imes 4 = 5 	imes 10^{-13} \ cm$. The radius of the atom is $R_{a} = 1 \ \mathring{A} = 10^{-8} \ cm$. The volume of the nucleus is $V_{n} = \frac{4}{3} \pi (R_{n})^3$ and the volume of the atom is $V_{a} = \frac{4}{3} \pi (R_{a})^3$. The fraction of volume occupied by the nucleus is $\frac{V_{n}}{V_{a}} = \frac{(R_{n})^3}{(R_{a})^3} = \left( \frac{5 	imes 10^{-13}}{10^{-8}} ight)^3 = (5 	imes 10^{-5})^3 = 125 	imes 10^{-15} = 1.25 	imes 10^{-13}$.

The radius of a nucleus with mass number $A$ is given by $1.25 \times 10^{-13} \times A^{1/3} \ cm$. If the radius of the atom is $1 \ \mathring{A}$ and the mass number is $64$,calculate the fraction of the volume occupied by the nucleus.

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