Select The Correct Answer.In A Fission Reaction Of U-235, There Was A Release Of $9.20 \times 10^{11} \text{ KJ}$ Of Energy. What Amount Of Mass In Kilograms Would Have Been Lost? Recall That $c=3 \times 10^8 \text{ M/s}$.A.

by ADMIN 229 views

Introduction

The concept of mass-energy equivalence, as described by Albert Einstein's famous equation E=mc^2, is a fundamental principle in physics that relates the energy of a system to its mass. In the context of nuclear reactions, such as fission, this principle is particularly relevant. Fission reactions involve the splitting of heavy atomic nuclei, resulting in a significant release of energy. In this article, we will explore how to calculate the amount of mass lost in a fission reaction, given the energy released.

The Mass-Energy Equivalence Equation

The mass-energy equivalence equation is given by:

E = mc^2

where E is the energy released, m is the mass lost, and c is the speed of light in vacuum. This equation shows that a certain amount of mass (m) can be converted into a corresponding amount of energy (E), and vice versa.

Calculating the Mass Lost

Given that the energy released in the fission reaction is $9.20 \times 10^{11} \text{ kJ}$, we can use the mass-energy equivalence equation to calculate the amount of mass lost. First, we need to convert the energy from kilojoules (kJ) to joules (J), since the speed of light is typically expressed in meters per second (m/s).

9.20×1011 kJ=9.20×1014 J9.20 \times 10^{11} \text{ kJ} = 9.20 \times 10^{14} \text{ J}

Now, we can plug in the values into the mass-energy equivalence equation:

E=mc2E = mc^2

9.20×1014 J=m×(3×108 m/s)29.20 \times 10^{14} \text{ J} = m \times (3 \times 10^8 \text{ m/s})^2

To solve for m, we can rearrange the equation:

m=Ec2m = \frac{E}{c^2}

m=9.20×1014 J(3×108 m/s)2m = \frac{9.20 \times 10^{14} \text{ J}}{(3 \times 10^8 \text{ m/s})^2}

m=9.20×1014 J9.00×1016 m2/s2m = \frac{9.20 \times 10^{14} \text{ J}}{9.00 \times 10^{16} \text{ m}^2/\text{s}^2}

m=1.02×10−2 kgm = 1.02 \times 10^{-2} \text{ kg}

Therefore, the amount of mass lost in the fission reaction is approximately 0.0102 kilograms.

Conclusion

In conclusion, the mass-energy equivalence equation is a powerful tool for calculating the amount of mass lost in a fission reaction, given the energy released. By plugging in the values into the equation, we can determine the exact amount of mass lost. In this case, we found that the amount of mass lost is approximately 0.0102 kilograms.

References

  • Einstein, A. (1905). Does the Inertia of a Body Depend Upon Its Energy Content? Annalen der Physik, 18(13), 639-641.
  • Feynman, R. P. (1963). The Feynman Lectures on Physics. Addison-Wesley.

Further Reading

  • Nuclear Fission: A Comprehensive Review
  • Mass-Energy Equivalence: A Fundamental Principle in Physics
  • The Energy-Mass Equivalence Equation: A Derivation
    Frequently Asked Questions (FAQs) on Mass-Energy Equivalence in Fission Reactions ====================================================================================

Q: What is the mass-energy equivalence equation?

A: The mass-energy equivalence equation is given by E = mc^2, where E is the energy released, m is the mass lost, and c is the speed of light in vacuum.

Q: How is the mass-energy equivalence equation used in fission reactions?

A: The mass-energy equivalence equation is used to calculate the amount of mass lost in a fission reaction, given the energy released. By plugging in the values into the equation, we can determine the exact amount of mass lost.

Q: What is the significance of the speed of light (c) in the mass-energy equivalence equation?

A: The speed of light (c) is a fundamental constant in physics that relates the energy of a system to its mass. In the mass-energy equivalence equation, c is squared, indicating that a small amount of mass can be converted into a large amount of energy.

Q: Can the mass-energy equivalence equation be used to calculate the energy released in a fission reaction?

A: Yes, the mass-energy equivalence equation can be used to calculate the energy released in a fission reaction, given the amount of mass lost. By rearranging the equation, we can solve for E.

Q: What is the relationship between mass and energy in a fission reaction?

A: In a fission reaction, a small amount of mass is converted into a large amount of energy. This is a direct result of the mass-energy equivalence equation, which shows that a certain amount of mass (m) can be converted into a corresponding amount of energy (E).

Q: Can the mass-energy equivalence equation be used in other types of nuclear reactions?

A: Yes, the mass-energy equivalence equation can be used in other types of nuclear reactions, such as fusion reactions. However, the equation is particularly relevant in fission reactions, where a large amount of energy is released.

Q: What are some real-world applications of the mass-energy equivalence equation?

A: The mass-energy equivalence equation has numerous real-world applications, including:

  • Nuclear power plants: The equation is used to calculate the energy released in fission reactions, which is then used to generate electricity.
  • Particle accelerators: The equation is used to calculate the energy of particles accelerated to high speeds.
  • Nuclear medicine: The equation is used to calculate the energy released in nuclear reactions, which is then used to treat cancer.

Q: Can the mass-energy equivalence equation be used to calculate the mass lost in a fusion reaction?

A: Yes, the mass-energy equivalence equation can be used to calculate the mass lost in a fusion reaction. However, the equation is typically used in fission reactions, where a large amount of energy is released.

Q: What is the difference between mass and energy in a fission reaction?

A: In a fission reaction, mass is converted into energy. This is a direct result of the mass-energy equivalence equation, which shows that a certain amount of mass (m) can be converted into a corresponding amount of energy (E).

Q: Can the mass-energy equivalence equation be used to calculate the energy released in a nuclear explosion?

A: Yes, the mass-energy equivalence equation can be used to calculate the energy released in a nuclear explosion. However, the equation is typically used in controlled nuclear reactions, such as those found in nuclear power plants.

Conclusion

In conclusion, the mass-energy equivalence equation is a fundamental principle in physics that relates the energy of a system to its mass. The equation has numerous real-world applications, including nuclear power plants, particle accelerators, and nuclear medicine. By understanding the mass-energy equivalence equation, we can better appreciate the complex relationships between mass and energy in fission reactions.