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Question

(D) Given: Mass number $A = 64$. Radius of nucleus $R_n = 1.25 	imes 10^{-13} 	imes (64)^{1/3} \, 	ext{cm} = 1.25 	imes 10^{-13} 	imes 4 \, 	ext

Vedclass · Accepted Answer

$1.25 	imes 10^{-13}$

Vedclass · Answer

(D) Given: Mass number $A = 64$. Radius of nucleus $R_n = 1.25 	imes 10^{-13} 	imes (64)^{1/3} \, 	ext{cm} = 1.25 	imes 10^{-13} 	imes 4 \, 	ext{cm} = 5.0 	imes 10^{-13} \, 	ext{cm}$. Atomic radius $R_a = 1 \, \mathring{A} = 10^{-8} \, 	ext{cm}$. Volume of nucleus $V_n = \frac{4}{3} \pi R_n^3$. Volume of atom $V_a = \frac{4}{3} \pi R_a^3$. Fraction of volume occupied = $\frac{V_n}{V_a} = \left( \frac{R_n}{R_a} ight)^3$. Fraction = $\left( \frac{5.0 	imes 10^{-13}}{10^{-8}} ight)^3 = (5.0 	imes 10^{-5})^3 = 125 	imes 10^{-15} = 1.25 	imes 10^{-13}$.

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