Question 344: Atoms & Nuclei

Question

Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6	imes10^{-27}$$ kg and radius of nucleus is $$1.5	imes10^{-15}~\mathrm{A^{1/3}}$$ m. The approximate ratio of the nuclear density and water density is $$n	imes10^{13}$$. The value of $$n$$ is __________.

Accepted Answer

Radius $=1.5 	imes 10^{-15} A^{1 / 3}$
$$
	ext { Volume }=\frac{4 \pi}{3} r^{3}
$$
Mass of nucleus $=\left(1.6 	imes 10^{-27}ight) \mathrm{A} \mathrm{kg}$
$$
	ext { Density of nucleus }=\frac{1.6 	imes 10^{-27} 	imes A}{\frac{4}{3} 	imes \pi 	imes\left(1.5 	imes 10^{-15} A^{\frac{1}{3}}ight)^{3}}
$$
$$
\begin{aligned}
& =\frac{1.6 	imes 3 	imes 8 	imes 10^{18}}{4 \pi 	imes 27} \\
& =\frac{32}{9 \pi} 	imes 10^{17}
\end{aligned}
$$
Density of water $=1000 \mathrm{~kg} / \mathrm{m}^{3}$
$\frac{	ext { Density of nucleus }}{	ext { Density of water }}=\frac{\frac{32}{9 \pi} 	imes 10^{17}}{1000}$
$=\frac{320}{9 \pi} 	imes 10^{13}$
$=11.32 	imes 10^{13}$
value of $n=11$

Atoms & Nuclei

Assume that protons and neutrons have equal masses. Mass of a nucleon is $1.6\times10^{-27} kg and radius of nucleus is 1.5\times10^{-15}~\mathrm{A^{1/3}} m. The approximate ratio of the nuclear density and water density is n\times10^{13}. The value of n$ is __________.

Integer / Numeric Answer Type