Chapter 30, Problem 68A

To determine

To calculate:

The mass of uranium $-235$ that underwent fission to produce energy of bomb.

Answer to Problem 68A

The mass of uranium $-235$ that underwent fission to produce energy of bomb is $289\text{kg}\text{.}$

Explanation of Solution

Given:

Number of moles

Formula Used:

Formula to calculate number of moles is $\frac{x}{6.022\times {10}^{23}\text{atoms/mole}}$

Formula to calculate number of atoms is $=x\text{moles}\times \frac{6.022\times {10}^{23}\text{atoms}}{1\text{mole}}$

Where,

  $x$ : Number of atoms

  $6.022\times {10}^{23}\text{atoms}$ : Avogadro’s Number

Calculation:

For uranium atom $-235$ ,

First calculate the number of atoms and moles,

To calculate number of atoms is $x\text{moles}\times \frac{6.022\times {10}^{23}\text{atoms}}{1\text{mole}}$

Substitute all the values in given formula,

  $=\frac{\left(2.0e1\right)\times \left(5.0e12\right)}{3.21e-11}=3.11526e24\text{atoms}$

Now to calculate the number of moles by using the formula, $\frac{x}{6.022\times {10}^{23}\text{atoms/mole}}$

Substitute all the values in given formula,

Now the number of atoms is obtained from the previous calculation.

Here, $x=3.11526e24\text{atoms}$

  $=\frac{3.11526e24}{6.02e23}=5.175\text{moles}$

As the molar mass of uranium is $55.937\text{kg/mol}$ .

Use formula to find the mass of uranium, $\left(\text{number}\text{of}\text{moles}\right)\text{×}\left(\text{molar}\text{mass}\right)$

  $=\left(5.175\right)\times \left(55.937\right)$

  $=289\text{kg}$

Conclusion:

Hence, the mass of uranium $-235$ that underwent fission to produce energy of bomb is $289\text{kg}$ .