Chapter 2, Problem 2.10E

Interpretation Introduction

(a)

Interpretation:

The charge and mass (in u) of nucleus made up of $4$ protons and $5$ neutrons are to be calculated

Concept introduction:

The three subatomic particles are electrons, neutrons and protons. Out of these three, neutrons and protons are located inside the nucleus of an atom. The electron carries a charge of $-1$, proton carries a charge of $+1$ and neutron does not carry any charge.

Answer to Problem 2.10E

The charge and mass (in u) of nucleus made up of $4$ protons and $5$ neutrons are $+4$ and $9\text{u}$ respectively.

Explanation of Solution

In a nucleus having $4$ protons and $5$ neutrons, the charge is only due to the protons as the neutron does not carry any charge. Thus, the charge for such a nucleus is equal to charge of protons which is equal to $+4$. The mass of nucleus is calculated by the formula given below.

${\text{M}}_{\text{nucleus}}={\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}$

Where,

• ${\text{M}}_{\text{nucleus}}$ is the mass of nucleus

• ${\text{M}}_{\text{proton}}$ is the mass of protons

• ${\text{M}}_{\text{neutron}}$ is the mass of neutrons

Mass of neutron and mass of proton in terms of atomic unit is $1\text{u}$ each.

Substitute the values in the above equation as follows.

$\begin{array}{rll}{\text{M}}_{\text{nucleus}}& =& {\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}\\ & =& \left(4\times 1\text{u}\right)+\left(5\times 1\text{u}\right)\\ & =& 9\text{u}\end{array}$

Thus, the mass of nucleus having $4$ protons and $5$ neutrons is $9\text{u}$.

Conclusion

The charge and mass (in u) of nucleus made up of $4$ protons and $5$ neutrons are calculated $+4$ and $9\text{u}$ respectively.

Interpretation Introduction

(b)

Interpretation:

The charge and mass (in u) of nucleus made up of $9$ protons and $10$ neutrons are to becalculated

Concept introduction:

The three subatomic particles are electrons, neutrons and protons. Out of these three, neutrons and protons are located inside the nucleus of an atom. The electron carries a charge of $-1$, proton carries a charge of $+1$ and neutron does not carry any charge.

Answer to Problem 2.10E

The charge and mass (in u) of nucleus made up of $9$ protons and $10$ neutrons are $+9$ and $19\text{u}$ respectively.

Explanation of Solution

In a nucleus having $9$ protons and $10$ neutrons, the charge is only due to the protons as the neutron does not carry any charge. Thus, the charge for such a nucleus is equal to charge of protons which is equal to $+9$. The mass of nucleus is calculated by the formula given below.

${\text{M}}_{\text{nucleus}}={\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}$

Where,

• ${\text{M}}_{\text{nucleus}}$ is the mass of nucleus

• ${\text{M}}_{\text{proton}}$ is the mass of protons

• ${\text{M}}_{\text{neutron}}$ is the mass of neutrons

Mass of neutron and mass of proton in terms of atomic unit is $1\text{u}$ each.

Substitute the values in the above equation as follows.

$\begin{array}{rll}{\text{M}}_{\text{nucleus}}& =& {\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}\\ & =& \left(9\times 1\text{u}\right)+\left(10\times 1\text{u}\right)\\ & =& 19\text{u}\end{array}$

Thus, the mass of nucleus having $9$ protons and $10$ neutrons is $19\text{u}$.

Conclusion

The charge and mass (in u) of nucleus made up of $9$ protons and $10$ neutrons are calculated as $+9$ and $19\text{u}$ respectively.

Interpretation Introduction

(c)

Interpretation:

The charge and mass (in u) of nucleus made up of $20$ protons and $23$ neutrons are to be calculated

Concept introduction:

The three subatomic particles are electrons, neutrons and protons. Out of these three, neutrons and protons are located inside the nucleus of an atom. The electron carries a charge of $-1$, proton carries a charge of $+1$ and neutron does not carry any charge.

Answer to Problem 2.10E

The charge and mass (in u) of nucleus made up of $20$ protons and $23$ neutrons are $+20$ and $43\text{u}$ respectively.

Explanation of Solution

In a nucleus having $20$ protons and $23$ neutrons, the charge is only due to the protons as the neutron does not carry any charge. Thus, the charge for such a nucleus is equal to charge of protons which is equal to $+20$. The mass of nucleus is calculated by the formula given below.

${\text{M}}_{\text{nucleus}}={\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}$

Where,

• ${\text{M}}_{\text{nucleus}}$ is the mass of nucleus

• ${\text{M}}_{\text{proton}}$ is the mass of protons

• ${\text{M}}_{\text{neutron}}$ is the mass of neutrons

Mass of neutron and mass of proton in terms of atomic unit is $1\text{u}$ each.

Substitute the values in the above equation as follows.

$\begin{array}{rll}{\text{M}}_{\text{nucleus}}& =& {\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}\\ & =& \left(20\times 1\text{u}\right)+\left(23\times 1\text{u}\right)\\ & =& 43\text{u}\end{array}$

Thus, the mass of nucleus having $20$ protons and $23$ neutrons is $43\text{u}$.

Conclusion

The charge and mass (in u) of nucleus made up of $20$ protons and $23$ neutrons are calculated as $+20$ and $43\text{u}$ respectively.

Interpretation Introduction

(d)

Interpretation:

The charge and mass (in u) of nucleus made up of $47$ protons and $60$ neutrons are to be calculated

Concept introduction:

The three subatomic particles are electrons, neutrons and protons. Out of these three, neutrons and protons are located inside the nucleus of an atom. The electron carries a charge of $-1$, proton carries a charge of $+1$ and neutron does not carry any charge.

Answer to Problem 2.10E

The charge and mass (in u) of nucleus made up of $47$ protons and $60$ neutrons are $+47$ and $107\text{u}$ respectively.

Explanation of Solution

In a nucleus having $47$ protons and $60$ neutrons, the charge is only due to the protons as the neutron does not carry any charge. Thus, the charge for such a nucleus is equal to charge of protons which is equal to $+47$. The mass of nucleus is calculated by the formula given below.

${\text{M}}_{\text{nucleus}}={\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}$

Where,

• ${\text{M}}_{\text{nucleus}}$ is the mass of nucleus

• ${\text{M}}_{\text{proton}}$ is the mass of protons

• ${\text{M}}_{\text{neutron}}$ is the mass of neutrons

Mass of neutron and mass of proton in terms of atomic unit is $1\text{u}$ each.

Substitute the values in the above equation as follows.

$\begin{array}{rll}{\text{M}}_{\text{nucleus}}& =& {\text{M}}_{\text{proton}}+{\text{M}}_{\text{neutron}}\\ & =& \left(47\times 1\text{u}\right)+\left(60\times 1\text{u}\right)\\ & =& 107\text{u}\end{array}$

Thus, the mass of nucleus having $47$ protons and $60$ neutrons is $107\text{u}$.

Conclusion

The charge and mass (in u) of nucleus made up of $47$ protons and $60$ neutrons are calculated as $+47$ and $107\text{u}$ respectively.