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Chapter 19: Problem 51

U-2 35 undergoes many different fission reactions. For one such reaction, when U- 235 is struck with a neutron, Ce- 144 and Sr90 are produced along with some neutrons and electrons. How many neutrons and \(\beta\) -particles are produced in this fission reaction?

Short Answer

Expert verified
In the fission reaction of U-235 involving the production of Ce-144 and Sr-90, there are 2 neutrons (\(n\)) and 4 beta particles (\(\beta^{-}\)) produced.

Step by step solution

01

Identify the reactants and products

The reactants are: - U-235 (an isotope of Uranium) as the target nucleus - Neutron that strikes U-235 The products are: - Ce-144 (an isotope of Cerium) - Sr-90 (an isotope of Strontium) - Unknown number of neutrons - Unknown number of beta particles The fission reaction can be represented as: \[n + _{92}^{235}U \rightarrow _{58}^{144}Ce + _{38}^{90}Sr + x\, n + y\, \beta^{-}\]
02

Apply conservation of nucleon number

The total number of nucleons (protons + neutrons) should be the same before and after the reaction. Since U-235 has 235 nucleons and the incoming neutron has 1, the total nucleon number on the left is 236. In the equation below, x is the number of neutrons and A1, A2 represent the nucleon numbers for Ce-144 and Sr-90, respectively: \[236 = A_1 + A_2 + x\] Since both A1 and A2 are known: A1 = 144 and A2 = 90, we can write: \[236 = 144 + 90 + x\]
03

Solve for the unknown number of neutrons x

Now, it's time to solve the equation for x: \[x = 236 - 144 - 90\] \[x = 2\] So, 2 neutrons are produced in this fission reaction.
04

Apply conservation of charge

The total charge on both sides of the reaction should be conserved. The initial charge on the left side is from U-235 itself since the incoming neutron has no charge. On the right side, y beta particles are produced. β⁻ particles are electrons, so each has a charge of -1. The equation can be written as: \[92 = 58 + 38 - y\]
05

Solve for the unknown number of Beta particles y

Now, we can solve the equation for y: \[y = 58 + 38 - 92\] \[y = 4\] So, 4 beta particles are produced in this fission reaction. In conclusion: In this fission reaction, when U-235 is struck with a neutron and results in the production of Ce-144 and Sr-90, there are 2 neutrons and 4 beta particles produced.

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