Chapter 30, Problem 69GP

To determine

To Estimate: The total binding energy of copper and energy in joules needed to break a copper penny.

Explanation of Solution

Given:

  $M\left(\text{C}\text{u}\right)=62.929601\text{u}$

Number of nucleons = 63

Calculations:

From the binding energy per nucleon versus mass number curve, the value for B.E. per nucleon of $\text{C}\text{u}$ is about $8.6\text{MeV}$ .

B.E energy of copper atom $=8.6\text{MeV}\times \text{63}\approx \text{542 MeV}$

Number of atoms in 3.0 g copper penny:

  $\begin{array}{c}N=n{N}_A\\ =\left(\frac{m}{M}\right)N_A\\ =\frac{\left(\text{3 g}\right)\left(\text{6}{\text{.022×10}}^{\text{23}}\text{atoms/mol}\right)}{\left(\text{63 g/mol}\right)}\\ =2.87\times {10}^{22}\text{atoms}\end{array}$

Here, m is the mass, M is the molar mass and $N_A$ is the Avogadro’s number.

Thus, to break the nucleons of 3.0 g copper penny, the required energy can be calculated as follows:

  $\begin{array}{l}E=\text{B}\text{.E×N}\\ E=\text{542}\text{MeV}\times 2.87\times {10}^{22}\\ E=\text{24}{\text{.7×10}}^{\text{22}}\text{MeV}\times \text{1}\text{.6}\times {\text{10}}^{-13}\frac{\text{J}}{\text{MeV}}\\ E=2.48\times {10}^{12}\text{J}\end{array}$

Conclusion:

Thus, the energy to break the nucleons of 3.0 g copper penny is $2.48\times {10}^{12}\text{J}$ .