Nuclear fission involves the splitting apart of a larger nucleus to form two smaller nuclei. Fission can be achieved by bombarding a heavy nucleus with high-energy particles such as neutrons.
3rd attempt
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Your answer should include both the nuclear charge and the mass number.
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Determine the identity of the unknown nuclide in the following nuclear fission reaction. Include both the nuclear charge and the mass number.
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The correct answer and explanation is:
To solve for the unknown nuclide in the given nuclear fission reaction, we first need to balance both the mass number (total number of protons and neutrons) and the nuclear charge (number of protons). Let’s analyze the problem step by step.
Given:
- Reaction: 92235U+01n→56141Ba+X+301n^{235}_{92}\text{U} + ^1_0\text{n} \rightarrow ^{141}_{56}\text{Ba} + X + 3^1_0\text{n} Here, XX represents the unknown nuclide.
Step 1: Calculate total mass number
The mass number of uranium (92235U^{235}_{92}\text{U}) is 235. A neutron (01n^1_0\text{n}) adds 1 to the total mass. Thus, the total initial mass number is: 235+1=236235 + 1 = 236
On the right-hand side of the equation:
- 56141Ba^{141}_{56}\text{Ba} contributes 141.
- Three neutrons (3×13 \times 1) contribute 3.
- The mass number of XX is unknown.
Balancing the mass number: 236=141+3+Mass number of X236 = 141 + 3 + \text{Mass number of } X Mass number of X=236−141−3=92\text{Mass number of } X = 236 – 141 – 3 = 92
Step 2: Calculate total nuclear charge
The nuclear charge (proton number) of uranium is 92. A neutron has no charge, so the total charge initially is: 9292
On the right-hand side:
- 56141Ba^{141}_{56}\text{Ba} contributes 56.
- The nuclear charge of XX is unknown.
Balancing the nuclear charge: 92=56+Nuclear charge of X92 = 56 + \text{Nuclear charge of } X Nuclear charge of X=92−56=36\text{Nuclear charge of } X = 92 – 56 = 36
Step 3: Identify XX
The nuclide with nuclear charge 36 is krypton (Kr\text{Kr}).
Final Answer:
The unknown nuclide is: 3692Kr^{92}_{36}\text{Kr}
Explanation :
Nuclear fission is a process where a heavy nucleus splits into two smaller nuclei, releasing energy and neutrons. In the given reaction, uranium-235 (92235U^{235}_{92}\text{U}) absorbs a neutron, becoming 92236U^{236}_{92}\text{U}, which is unstable. This unstable nucleus splits into two smaller nuclei, barium-141 (56141Ba^{141}_{56}\text{Ba}) and krypton-92 (3692Kr^{92}_{36}\text{Kr}), along with three free neutrons.
To identify the unknown nuclide XX, we balance the reaction by ensuring both the total mass number and nuclear charge are conserved. The mass number represents the sum of protons and neutrons, while the nuclear charge reflects the number of protons (which defines the element). By subtracting the contributions of the known fragments (56141Ba^{141}_{56}\text{Ba} and the three neutrons) from the total, we determine the mass and charge of the missing component.
The calculated mass number of 92 and nuclear charge of 36 uniquely correspond to krypton (Kr\text{Kr}) in the periodic table. This reaction exemplifies how energy is released during fission because the total binding energy of the fission products is greater than that of the original heavy nucleus, with the difference manifesting as kinetic energy and gamma radiation.