### Atomic Physics Question 1

#### Question 1 - 24 January - Shift 1

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

## Show Answer

#### Answer: (11)

#### Solution:

density of nuclei $=\frac{\text{ mass of nuclei }}{\text{ volume of nuclei }}$

$ \begin{aligned} & \rho=\frac{1.6 \times 10^{-27} A}{\frac{4}{3} \pi(1.5 \times 10^{-15})^{3} A} \\ & =\frac{1.6 \times 10^{-27}}{14.14 \times 10^{-45}}=0.113 \times 10^{18} \end{aligned} $

$\rho_w=10^{3}$

Hence $\rho_w$

$ \frac{\rho}{\rho}=11.31 \times 10^{13} $