Is E=mc² Truly Equivalent to kE=(π)r² in Energy-Mass-Volume Relationships?

[Andy Lee]

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?

 

[Drakkith]

Is number 2 even correct? If I add one neutron to hydrogen to make deuterium, is the nuclear now bigger in volume?

 

[Dale]

The relationship between volume and mass in a nucleus is not as simple as just a proportionality.

http://en.wikipedia.org/wiki/Semi-empirical_mass_formula

 

[Andy Lee]

Thanks, that helps.

 

[DrGreg]

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).

 

[Myslius]

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

 

[mfb]

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.

 

[Fredster1765]

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.