College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Nuclear Reaction Q-Value Calculation
Imagine the following nuclear reaction:
\[ \mathbf{^{28}_{14}Si + ^{4}_{2}He \rightarrow ^{32}_{16}S} \]
Its Q-value is: Q = \_\_\_\_\_\_\_\_\_\_\_ MeV.
---
**Explanation and Calculations:**
The described nuclear reaction involves the silicon-28 nucleus (\( ^{28}_{14}Si \)) and a helium-4 nucleus (\( ^{4}_{2}He \)) producing a sulfur-32 nucleus (\( ^{32}_{16}S \)).
To find the Q-value, which represents the amount of energy released or absorbed during the nuclear reaction, we can use the mass-energy equivalence principle. The Q-value can be calculated using the mass of the reactants and products involved in the reaction.
### Steps to Calculate Q-Value:
1. **Determine the Masses:** Find the atomic masses (or nuclear masses) of the isotopes involved in the reaction.
- Mass of \( ^{28}_{14}Si \)
- Mass of \( ^{4}_{2}He \) (also known as an alpha particle)
- Mass of \( ^{32}_{16}S \)
2. **Apply the Mass-Energy Equivalence Formula:**
\[ Q = ( \text{mass of reactants} - \text{mass of products} ) \times 931.5 \text{ MeV/c}^2 \]
3. **Calculate:** Insert the mass values into the formula to find the Q-value. If the resulting Q-value is positive, it indicates an exothermic reaction (releases energy). If negative, it indicates an endothermic reaction (absorbs energy).
The placeholder ( \_\_\_\_\_\_\_\_\_\_\_ MeV ) is where you would insert the calculated Q-value.
### Educational Notes:
- **Nuclear Reactions:** These involve changes in an atom's nucleus and usually release much more energy than chemical reactions.
- **Isotopes:** Atoms of the same element with different numbers of neutrons.
- **Q-Value Importance:** Essential for understanding the energetics of nuclear processes, relevant in fields like nuclear physics, astrophysics, and energy production.
For an accurate calculation, make sure to use precise atomic mass units (amu) for each isotope, which](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29a56c7d-a09e-470c-8cf2-2ad52b8d7c92%2F7a0685fe-4325-4b16-8582-39f944c832d4%2Fnld5plb.png&w=3840&q=75)
Transcribed Image Text:### Nuclear Reaction Q-Value Calculation
Imagine the following nuclear reaction:
\[ \mathbf{^{28}_{14}Si + ^{4}_{2}He \rightarrow ^{32}_{16}S} \]
Its Q-value is: Q = \_\_\_\_\_\_\_\_\_\_\_ MeV.
---
**Explanation and Calculations:**
The described nuclear reaction involves the silicon-28 nucleus (\( ^{28}_{14}Si \)) and a helium-4 nucleus (\( ^{4}_{2}He \)) producing a sulfur-32 nucleus (\( ^{32}_{16}S \)).
To find the Q-value, which represents the amount of energy released or absorbed during the nuclear reaction, we can use the mass-energy equivalence principle. The Q-value can be calculated using the mass of the reactants and products involved in the reaction.
### Steps to Calculate Q-Value:
1. **Determine the Masses:** Find the atomic masses (or nuclear masses) of the isotopes involved in the reaction.
- Mass of \( ^{28}_{14}Si \)
- Mass of \( ^{4}_{2}He \) (also known as an alpha particle)
- Mass of \( ^{32}_{16}S \)
2. **Apply the Mass-Energy Equivalence Formula:**
\[ Q = ( \text{mass of reactants} - \text{mass of products} ) \times 931.5 \text{ MeV/c}^2 \]
3. **Calculate:** Insert the mass values into the formula to find the Q-value. If the resulting Q-value is positive, it indicates an exothermic reaction (releases energy). If negative, it indicates an endothermic reaction (absorbs energy).
The placeholder ( \_\_\_\_\_\_\_\_\_\_\_ MeV ) is where you would insert the calculated Q-value.
### Educational Notes:
- **Nuclear Reactions:** These involve changes in an atom's nucleus and usually release much more energy than chemical reactions.
- **Isotopes:** Atoms of the same element with different numbers of neutrons.
- **Q-Value Importance:** Essential for understanding the energetics of nuclear processes, relevant in fields like nuclear physics, astrophysics, and energy production.
For an accurate calculation, make sure to use precise atomic mass units (amu) for each isotope, which
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