Chapter 19, Problem 38A

Interpretation Introduction

Interpretation: Defining critical mass in fission reaction. Explaining whether a chain reaction can occur or not when sample has less than critical mass.

Concept introduction:

The balanced equation for fission reaction: ${}_{\text{ 92}}^{\text{ 235}}\text{U}+{}_0^{\text{1}}n\to {}_{56}^{140}\text{Ba }+{}_{36}^{93}\text{Kr}+{\text{ 3}}_0^{\text{1}}n$

In the fission processseveral neutrons emitted which can leads to the possibility of a chain reaction. Say, if at least one of the fission neutrons again undergoes fission with another fissile nucleus ${}_{\text{ 92}}^{\text{ 235}}\text{U}$ , which in turn cause nuclear fissions and emits neutrons to continue the chain reaction.

The critical mass is the minimum mass of fissile material needed for a nuclear chain reaction to become self-sustaining.

Answer to Problem 38A

No, chain reaction cannot occur when sample has less than critical mass.

Explanation of Solution

Although two to three neutrons are produced in each fission reaction, not all of these neutrons can cause another fission reaction. Some escape from the reaction vessel, some interact with non-fissile atomic nuclei.

For the fission process to be self-sustaining, at least one neutron from eachfission event must split another nucleus of ${}_{\text{ 92}}^{\text{ 235}}\text{U}$ . If, on the average, less than one neutron causes another fission event, the process stops. If exactly one neutron from each fission event causes another fission event then the process is self-sustaining. If more than one neutron from each fission event causes another fission reaction, the process rapidly accelerates and causes a violent explosion.

If the sample has less than critical mass too many neutrons escape before they have a chance to undergo fission with fissile nuclei and hence the process stops.

Conclusion

No, chain reaction cannot occur when sample has less than critical mass.