Chapter 20, Problem 21QP

Interpretation Introduction

Interpretation:

The mass of single ${}^{48}\text{Cr}$ is to be calculated with given nuclear binding energy of ${}^{48}\text{Cr}$.

Concept introduction:

Mass of one atom is equal to the mass of total protons, neutrons, and mass defect.

Mass defect refers to difference in the mass of an atom and the sum of mass of protons, electrons, and neutrons present in the atom.

Energy is given by the following expression:

$\Delta E=\Delta m{\text{c}}^{\text{2}}$

Here, $\text{Δm}$ represents mass defect and $\text{ΔE}$ is the nuclear binding energy.

The number of neutrons is calculated as

$\text{Number of neutron = Mass number}-\text{Number of proton}$

The number of nucleons is calculated as

$\text{Number of nucleon }=\text{Number of proton}+\text{Number of neutron }$

The relationship between and can be represented as

$\text{1 Kg}\text{=}\text{6}{\text{.022 ×10}}^{\text{26}}\text{amu}$

To convert the mass from amu to kilograms, conversion factor is

$\frac{\text{1 Kg}}{\text{6}{\text{.022 ×10}}^{\text{26}}\text{amu}}$.

The mass of atom is calculated as

$m=n_p{m}_p+n_n{m}_n-\Delta m$

Here, $n_p$ is number of proton, $m_p$ is mass of proton, $n_n$ is number of neutrons, $m_n$ is mass of neutrons, and $\Delta m$ is mass defect.