Chapter 30, Problem 10STP

To determine

To Calculate: The uranium- $235$ nuclei are required in a nuclear fission weapon.

Answer to Problem 10STP

  $2.5\times {10}^{24}.$

Explanation of Solution

Given:

Uranium- $235$ energy

$=3.2\times {10}^{-11}\text{J}$

Required TNT

$=20000tons$

1-ton TNT energy $=4\times {10}^{9}J.$

Formula used:

Required U- $235$= $\frac{\text{total energy released for 20000-ton TNT}}{\text{energy released by single U-235}}$

Calculation:

In the given data, Uranium- $235$ releases the energy $=3.2\times {10}^{-11}\text{J}$

1-ton TNT releases the energy $=4\times {10}^{9}J.$

20000-ton TNT release = how many joules of energy

Joules of energy released $\begin{array}{l}=20000\times 4\times {10}^{9}J\hfill \\ =8\times {10}^{13}J.\hfill \end{array}$

1 uranium - $235$ releases = $3.2\times {10}^{-11}J$

Required U- $235$ = $8\times {10}^{13}J.$

Required U- $235$ = $\frac{8\times {10}^{13}}{3.2\times {10}^{-11}}$

Required U- $235$ = $2.5\times {10}^{24}$

Conclusion:

  $2.5\times {10}^{24}$ Uranium- $235$ nuclei required in a nuclear fission weapon that releases energy equivalent to $20,000tons$ of TNT.