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Difficulty: MediumNuclear Fission and Nuclear Fusion
Consider the nuclear fission reaction represented by the equation below:
92235U+01n→56144Ba+3689Kr+x 01n{^{235}_{92}\text{U}} + {^{1}_{0}\text{n}} \rightarrow {^{144}_{56}\text{Ba}} + {^{89}_{36}\text{Kr}} + x\,^{1}_{0}\text{n}
What is the value of xx, representing the number of neutrons emitted in this reaction?
  1. A
    1
  2. B
    2
  3. 3Answer
  4. D
    4

Answer

The number of emitted neutrons, xx, is equal to 3.
By the law of conservation of mass number, the sum of nucleon numbers on the left side (235+1=236235 + 1 = 236) must equal the sum on the right side (144+89+x144 + 89 + x). Solving the equation 236=233+x236 = 233 + x gives x=3x = 3.

Step-by-Step Solution

1
Calculate the total mass number on the reactant side.
Total reactant mass number = 235+1=236235 + 1 = 236.
According to the law of conservation of nucleon number, the total mass number before the reaction must equal the total mass number after the reaction.
2
Sum the known mass numbers on the product side.
Known product mass number = 144+89=233144 + 89 = 233.
Adding the mass numbers of Barium-144 and Krypton-89.
3
Set up and solve the mass conservation equation for xx.
236=233+x(1)  ⟹  x=3236 = 233 + x(1) \implies x = 3.
Each neutron has a mass number of 1, so solving 236−233236 - 233 gives x=3x = 3.

Key Concept

Conservation of Mass Number in Nuclear Fission
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Topics

Nuclear Fission and Nuclear Fusion

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