Entery level Mass-energy equivalence questions

In summary: Set up an equation with all of these values and solve for the rest mass of X.In summary, the given scenario involves a proton with a kinetic energy of (0.178)(10-12)J colliding with a stationary nucleus X, resulting in the splitting of X into two alpha particles with equal kinetic energies of (1.481)(10-12)J. The mass equivalence of the net energy release during the collision can be calculated by finding the difference between the initial and final kinetic energies and converting it to a mass equivalent using E=mc2. To calculate the rest mass of nucleus X, the increase in kinetic energy must have come from a reduction in rest mass. By setting up an equation with the given values for the rest
  • #1
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Homework Statement


The diagram shows a proton moving with Ek of (0.178)(10-12)J towards a stationary nucleus X. The proton hits X and is absorbed.

The resulting nucleus splits into two alpha particles, which move off in the directions shown with equal Ek of (1.481)(10-12)J

1. Calculate the mass equivalence of the net energy release during the collision.
2. Calculate the rest mass of the nucleus X. The mass of a proton is (1.673)(10-27) kg and the mass of an alpha particle is (6.645)(10-27)kg

Homework Equations


E=mc2

The Attempt at a Solution


First question I have no idea how to do that.

second question, I simply added the proton mass + alpha particle mass (which is a wrong answer since energy is used for binding energy)

I sort of get the concepts but can't do them mathematically...
Please help me step by step.
Answers:
1. 3.09X10-29
2. 11.6X10-27
 
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  • #2
The guiding principle is mass/energy conservation.

initial (rest mass energy + kinetic energy)= final (rest mass energy + kinetic energy)

Question 1 is just concerned with the increase of kinetic energy expressed as a mass equivalence.
Question 2 just use the above equation. Be careful to include all rest masses and kinetic energies and express them all in the same unit.
 
  • #3
Sorry, I really do not know how to do these questions...
 
  • #4
For question 1 find the difference between the initial kinetic energy and the final kinetic energy. Then use E=mc^2 to convert energy to a mass equivalent.
 
  • #5
Thank you I've finally got and understood the first question.
I still don't know how to solve the second question... :/
 
  • #6
The increase in kinetic energy must have come from a reduction in rest mass. In other words the mass of the two alphas is less than the mass of X and the proton. You have values for the rest mass of the alphas and the proton and the mass equivalent of the kinetic energy gained.
 

1. What is the concept of mass-energy equivalence?

The concept of mass-energy equivalence states that mass and energy are two forms of the same thing and are interchangeable. This means that any amount of energy can be converted into an equivalent amount of mass and vice versa.

2. How did Albert Einstein discover mass-energy equivalence?

Einstein discovered mass-energy equivalence through his famous equation E=mc^2, where E represents energy, m represents mass, and c represents the speed of light. He developed this equation in his theory of relativity and it revolutionized the understanding of the relationship between mass and energy.

3. What is the significance of mass-energy equivalence?

The significance of mass-energy equivalence is that it provided a new understanding of the fundamental nature of matter and energy. It also led to the development of nuclear energy and nuclear weapons, which have greatly impacted society and technology.

4. How is mass-energy equivalence applied in practical situations?

Mass-energy equivalence is applied in practical situations in various fields, such as nuclear energy, medical imaging, and particle accelerators. In nuclear energy, the conversion of mass into energy is used to generate electricity. In medical imaging, the conversion of energy into mass is used to create images of the body. In particle accelerators, the conversion of mass into energy is used to create high-energy particles for research purposes.

5. What are some misconceptions about mass-energy equivalence?

One common misconception about mass-energy equivalence is that it implies that mass can be completely converted into energy, leading to the idea of perpetual motion. However, this is not possible as there is always a conservation of mass and energy. Another misconception is that the equation E=mc^2 only applies to nuclear reactions, but it actually applies to all forms of energy and mass.

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