The mass which is lost is very small and we know we can't divide protons or Neutrons. Then how come mass change is very less. Is proton disintegrated? I'm really confused as a high school student. Please help me .
Asked
Active
Viewed 47 times
1 Answers
1
So negative binding energy is an important concept in physics, but nuclei mayn't be the best place to start. There pro's are: binding energy is a significant fraction of rest mass energy, but the con's are: it's a strongly coupled quantum system.
So let's do a simple classical example. You have two attracting magnets (mass $m$), in one dimension. Let's call them $N$ and $S$.
When they are infinitely separated, the total energy of the system is the sum of there rest mass energies.
$$ E_{\infty} = mc^2 + mc^2 = 2mc^2 $$
Now imagine them in a bound state. For simplicity, we'll say their fields (these are pretend magnets) cause a constant attractive force $F$ out to a distance $R$, and zero thereafter. The have some total energy:
$$ E_0 = M_{mm}c^2 $$
that is equivalent to a rest mass.
The binding energy is the energy required to go from the bound configuration to the unbound configuration. We can calculate that by imagining pulling them apart slowly:
Pulling them apart requires doing work. You have to pull against the attractive force. Work is force times distance, which for this case is:
$$ W = FR \equiv E_{binding} $$
so that:
$$ E_0 + W = E_{\infty} $$
Then:
$$ Mc^2 = 2mc^2 - E_{binding} $$
or
$$ M = 2m - \frac{E_{binding}}{c^2} $$
What this means is mass is not stuff. Mass is energy (with a scaling factor). Your question seems to associate mass exactly with baryon number (which is number of protons plus number of neutrons).
Baryon number is exactly conserved, and is countable in indivisible. Mass is not.
JEB
- 42,131