Chapter 7.3, Problem 6GP

To determine

To find the mass number A of an atom.

Answer to Problem 6GP

1.44

Explanation of Solution

Given:

Radius: $r=1.2A^{\frac{1}{3}}$

  $r=3.6\text{ femtometers}$

Calculation:

The radius r of the nucleus of an atom of mass number A is,

  $r=1.2A^{\frac{1}{3}}$

Given that the radius r is 3.6 femtometers.

Substituting the values of r in the expression,

  $\Rightarrow 3.6=1.2A^{\frac{1}{3}}$

Dividing 1.2 on both sides,

  $\begin{array}{l}\Rightarrow \frac{3.6}{1.2}=\frac{1.2}{1.2}{A}^{\frac{1}{3}}\\ \Rightarrow 3=A^{\frac{1}{3}}\end{array}$

Taking cube root on both sides,

  $\begin{array}{l}\Rightarrow \sqrt[3]{3}=\sqrt[3]{A^{\frac{1}{3}}}\\ \Rightarrow A=\sqrt[3]{3}\\ \Rightarrow A=1.44\end{array}$

Conclusion:

Therefore, the mass number of the atom is 1.44.