e=mc^2 question

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?

DaleSpam

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

http://en.wikipedia.org/wiki/Semi-em...l_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 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.

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Andy Lee	e=mc^2 question Tweet 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 Recognitions: Gold Member	Is number 2 even correct? If I add one neutron to hydrogen to make deuterium, is the nuclear now bigger in volume?

DaleSpam Mentor	The relationship between volume and mass in a nucleus is not as simple as just a proportionality. http://en.wikipedia.org/wiki/Semi-em...l_mass_formula

DrGreg Recognitions: Gold Member Science Advisor	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).

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.

Fredster1765	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.