Chapter 4, Problem 79A

Interpretation Introduction

Interpretation : The mass defect of a chlorine-35 atom is to be calculated.

Concept Introduction : The total masses of the component particles that make up an atom are always greater than the mass of the atom itself. The term "mass defect" refers to the missing mass. The formula of mass defect $\Delta m$ is given as

  $\Delta m=\left[Z\left(m_p+m_e\right)+\left(A-Z\right)m_n\right]-m_{atom}$

Where, $Z$ is the atomic number, $A$ is the mass number, $m_p$ is the mass of the proton, $m_e$ is the mass of the electron, and $m_n$ is the mass of the neutron.

Answer to Problem 79A

The mass defect of a chlorine-35 atom is $4.70\times {10}^{-25}\text{g}$ .

Explanation of Solution

Given information:

The actual mass of chlorine-35 atom is $5.81\times {10}^{-23}\text{g}$ .

There are 17 protons and 17 electrons in chlorine atom.

The mass of proton is $1.67\times {10}^{-24}\text{g}$ .

The mass of electron is $9.11\times {10}^{-28}\text{g}$ .

The mass of neutron is $1.67\times {10}^{-24}\text{g}$ .

The mass defect indicates the matter that was transformed into energy when the nucleus was created from its component protons and neutrons.

The formula of mass defect is given as:

  $\Delta m=\left[Z\left(m_p+m_e\right)+\left(A-Z\right)m_n\right]-m_{atom}$

Where, $Z$ is the atomic number, $A$ is the mass number, $m_p$ is the mass of the proton, $m_e$ is the mass of the electron, and $m_n$ is the mass of the neutron.

To calculate the mass defect of chlorine-35 atom, substitute the values in the above formula:

  $\begin{array}{c}\Delta m=\left[Z\left(m_p+m_e\right)+\left(A-Z\right)m_n\right]-m_{atom}\\ =\left[17\left(\left(1.67\times {10}^{-24}\text{g}\right)+\left(9.11\times {10}^{-28}\text{g}\right)\right)+\left(35-17\right)\left(1.67\times {10}^{-24}\text{g}\right)\right]-5.81\times {10}^{-23}\text{g}\\ =4.70\times {10}^{-25}\text{g}\end{array}$