# E=mc^2 question

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

Thanks, that helps.

DrGreg
Gold Member
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).

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
Mentor
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.

If 2. were correct I dont 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.