Energy, Mass, & Volume: Exploring the Equivalence of E=mc^2

In summary, the conversation discusses the relationship between energy, mass, and volume in a nucleus. While it is commonly known that energy is proportional to mass, the direct relationship between mass and volume is not as simple. The idea of determining volume from a cross-sectional area is questioned, as it may not accurately reflect the true volume of the nucleus. Additionally, the conversation mentions the difficulties in calculating the mass-radius relationship for a nucleus, and speculates on the implications of the incorrect assumption that mass is proportional to volume.
  • #1
Andy Lee
37
0
1. Energy is proportional to mass.
2. Mass (of nucleus) is proportional to volume.
3. Volume can be determined from cross-sectional area.

If this is the case, then is E=mc^2 equivalent to kE=(pi)r^2 where r is the radius of the nucleus and k is some constant?
 
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  • #2
Is number 2 even correct? If I add one neutron to hydrogen to make deuterium, is the nuclear now bigger in volume?
 
  • #4
Thanks, that helps.
 
  • #5
Even if (2) were true (and DaleSpam has pointed out it isn't), you would expect an r3 term, not an r2 term. (Volume of a sphere isn't proportional to area).
 
  • #6
2. Mass = Volume x Density

What's the idea to measure volume of as a cross section anyway?
Volume of n-sphere can be easily calculated without any cross sectional area using formulas.
Cross section of 4D objects is 3D object.

I have no idea how to calculate mass-radius relationship for nucleus, it's difficult because it's a compound, but for example mass of electron = coupling * Planck's mass * Planck's length / classical electron radius
 
  • #7
I think Andy Lee meant the two-dimensional cross-section which can be observed in particle physics - this can be used to estimate the volume of the nucleus.
 
  • #8
If 2. were correct I don't think atomic bombs would exist (at least not in the way they do in this universe!) since the energy as I understand it comes from the difference in mass of the nucleus and the constituents of the nucleus, so if they were proportional there wouldn't be any release of excess energy.
 

1. What is the significance of the equation E=mc^2?

The equation E=mc^2 is one of the most famous and important equations in physics. It describes the relationship between energy (E), mass (m), and the speed of light (c). It means that mass and energy are interchangeable and can be converted into one another.

2. How does the equation E=mc^2 relate to the concept of mass-energy equivalence?

The equation E=mc^2 is a representation of the concept of mass-energy equivalence, which is a key principle in physics. It means that mass and energy are different forms of the same thing and can be converted into one another. This concept is important in understanding the behavior of particles at high speeds and in nuclear reactions.

3. Can you give an example of the conversion of mass into energy?

One example of the conversion of mass into energy is in nuclear reactions, such as in a nuclear power plant or a nuclear bomb. In these reactions, a small amount of mass is converted into a large amount of energy, as predicted by the equation E=mc^2. This is because the nuclei of atoms are split or fused together, releasing a tremendous amount of energy.

4. How does the equation E=mc^2 relate to the concept of conservation of energy?

The equation E=mc^2 is closely related to the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another. The equation shows that mass and energy are two forms of the same thing and can be converted into one another, but the total amount of energy remains constant.

5. What are the implications of the equation E=mc^2 in everyday life?

The equation E=mc^2 has many practical applications in everyday life. It is the basis for nuclear power and nuclear weapons, and it also plays a role in medical imaging techniques like PET scans. It also helps us understand the behavior of particles in high-speed collisions, such as those in particle accelerators. Additionally, the equation has been used to develop technologies like nuclear energy and nuclear medicine that have greatly impacted our society.

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