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13.Nuclei
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Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6 \times 10^{-27}\,kg$ and radius of nucleus is $1.5 \times 10^{-15} A ^{1 / 3}\,m$. The approximate ratio of the nuclear density and water density is $n \times 10^{13}$. The value of $n$ is $.................$
A
$11$
B
$12$
C
$14$
D
$16$
(JEE MAIN-2023)
Solution
$\text { density of nuclei }=\frac{\text { mass of nuclei }}{\text { volume of nuclei }}$
$\rho=\frac{1.6 \times 10^{-27} A }{\frac{4}{3} \pi\left(1.5 \times 10^{-15}\right)^3 A } $
$=\frac{1.6 \times 10^{-27}}{14.14 \times 10^{-45}}=0.113 \times 10^{18}$
$\rho_{ W }=10^3$
$\text { Hence } \frac{\rho}{\rho_w}=11.31 \times 10^{13}$
Standard 12
Physics
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