Assume that protons and neutrons have equal masses. Mass of a nucleon is and radius of nucleus is . The approximate ratio of the nuclear density and water density is . The value of is _______. [2023]

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Solution

Q.
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 _______. [2023]

Ans.
(11)

$Density of nuclei = \frac{mass of nuclei}{volume of nuclei}$

$ρ = \frac{1.6 \times 10^{- 27} A}{\frac{4}{3} π {(1.5 \times 10^{- 15})}^{3} A} = 0.113 \times 10^{18} {kg/m}^{3}$

$ρ_{w} = 10^{3} {kg/m}^{3}$

$Hence \frac{ρ}{ρ_{w}} = 11.31 \times 10^{13}$

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