Chapter 24, Problem 95A

(a)

Interpretation Introduction

Interpretation:

Mass of the nucleon should be calculated.

Concept introduction:

Nucleon is a term specifically used for protons and neutrons present in an atom. Difference between the mass of the nucleus and mass of the nucleon is referred to as mass defect. When 1 mole of nucleus breaks into its constituent nucleons, the energy required is known as binding energy.

Answer to Problem 95A

Mass of the nucleon in deuterium isotope is $2.016606\text{amu}$.

Explanation of Solution

Given information:

Mass of proton or hydrogen is $1.007941\text{amu}$, mass of neutron is $1.008665\text{amu}$ and mass of deuterium is $\text{2}\text{.014102}\text{amu}$.

The formula to calculate mass of nucleon is as follows:

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

Substitute $1.007941\text{amu}$ for mass of proton and $1.008665\text{amu}$ for mass of neutron in above equation.

$\begin{array}{c}\text{mass}\text{of}\text{nucleon}=\text{mass}\text{of}\text{proton}+\text{mass}\text{of}\text{neutron}\\ =1.007941\text{amu}+1.008665\text{amu}\\ =2.016606\text{amu}\end{array}$

Mass of the nucleon in deuterium isotope is $2.016606\text{amu}$.

(b)

Interpretation Introduction

Interpretation:

Mass defect associated with deuterium should be calculated.

Concept introduction:

Nucleon is term specifically used for protons and neutrons present in an atom. Difference between the mass of the nucleus and mass of the nucleon is referred to as mass defect. When 1 mole of nucleus breaks into its constituent nucleons the energy required is known as binding energy.

Answer to Problem 95A

Mass defect for deuterium is $0.002504\text{amu}$.

Explanation of Solution

Given information:

Mass of proton or hydrogen is $1.007941\text{amu}$, mass of neutron is $1.008665\text{amu}$ and mass of deuterium is $\text{2}\text{.014102}\text{amu}$.

The formula to calculate mass defect is as follows:

$\text{mass}\text{defect}=m_{\text{nucleus}}-\left[N_{\text{p}}{m}_{\text{p}}+N_{\text{n}}{m}_{\text{n}}\right]$

Where,

$m_{\text{nucleus}}$ is mass of the nucleus.

$N_{\text{p}}$ is number of protons.

$m_{\text{p}}$ is mass of proton.

$N_{\text{n}}$ is number of neutrons.

$m_{\text{n}}$ is mass of neutron.

Substitute $1.007941\text{amu}$ for $m_{\text{p}}$, $1.008665\text{amu}$ for $m_{\text{n}}$, 1 for $N_{\text{p}}$, 1 for $N_{\text{n}}$ and $\text{2}\text{.014102}\text{amu}$ for $m_{\text{nucleus}}$ in above equation.

$\begin{array}{c}\left|\text{mass}\text{defect}\right|=m_{\text{nucleus}}-\left[N_{\text{p}}{m}_{\text{p}}+N_{\text{n}}{m}_{\text{n}}\right]\\ =\text{2}\text{.014102}\text{amu}-\left[\left(1\right)\left(1.007941\text{amu}\right)+\left(1\right)\left(1.008665\text{amu}\right)\right]\\ =\left|-0.002504\right|\text{amu}\\ =0.002504\text{amu}\end{array}$

Mass defect for deuterium is $0.002504\text{amu}$.

(c)

Interpretation Introduction

Interpretation:

Binding energy for deuterium should be calculated.

Concept introduction:

Nucleon is term specifically used for protons and neutrons present in an atom. Difference between the mass of the nucleus and mass of the nucleon is referred to as mass defect. When 1 mole of nucleus breaks into its constituent nucleons the energy required is known as binding energy.

Answer to Problem 95A

Binding energy for deuterium is $2.3324\text{MeV}$.

Explanation of Solution

Given information:

Mass of proton or hydrogen is $1.007941\text{amu}$, mass of neutron is $1.008665\text{amu}$ and mass of deuterium is $\text{2}\text{.014102}\text{amu}$.

Conversion factor for $\text{amu}$ to $\text{MeV}$ is as follows:

$1\text{amu}\text{=}\text{931}\text{.49}\text{MeV}$

Mass defect for deuterium is $0.002504\text{amu}$ which in terms of $\text{MeV}$ is

$\begin{array}{c}0.002504\text{amu}=\left(\frac{\text{931}\text{.49}\text{MeV}}{1\text{amu}}\right)0.002504\text{amu}\\ =2.3324\text{MeV}\end{array}$

Binding energy for deuterium is $2.3324\text{MeV}$.