My textbook says that: “in stable isotopes, strong nuclear forces are greater than the electrostatic forces”.
Doesn’t that imply that, the more neutrons a nucleus has, the stronger this strong nuclear force will get, so it’s always a win if we have more neutrons?
The definition of beta decay is also stated as “occurs if the nucleus has too many neutrons to be stable”. How and when would this ever be a case? The two definitions seem contradicting
In: Physics
Your conclusion from the text book paragraph is incorrect. All that statement says is “stable isotopes are stable because the strong nuclear force is larger than the electrostatic force” you forget that the strong force drops off very quickly with distance, so adding more and more neutrons decreases the overall strong force, making the electrostatic force become more dominant.
Strong nuclear forces bind neutrons to neutron, protons to protons, and neutrons to protons.
In the simplest approximation of the nucleus, neutrons and protons are identical except for a quantum number called isospin. Because their isospin is different, neutrons and protons have independent energy levels. The neutrons fill in their energy levels starting at the lowest level, regardless of the protons, and vice versa. So if there’s more neutrons than protons, the neutron in the highest occupied neutron energy level is at a higher level than the proton in the highest occupied proton energy level.
So it can be energetically favorable for that neutron to “flip” isospin, becoming a proton, and drop down to the lowest unoccupied proton level. That “flip” process occurs through the weak nuclear force and results in the creation of a beta and neutrino.
In stable heavy nuclei, there are more neutrons than protons. The reason is that you also have to account for the extra energy from proton-proton electromagnetic repulsion. So the simple model where the neutron energy levels and proton energy levels are identical is wrong… The proton energy level is higher than the corresponding neutron energy level. So you can get a situation like Fe56 being stable with 26 protons and 30 neutrons. The 30th neutron is at an energy similar to the 26th proton, and it would take extra energy to flip it into a 27th proton.
Fe57 and Fe58 (31 and 32 neutrons) are also stable. Beyond the simple model I described, there are other effects like spin pairing and uneven spacing between energy levels due to she’ll effects. (This is very similar to why noble gasses are chemically stable).
But at Fe59, that 33rd neutron is up so high it can flip into being a proton and emit energy by beta decay
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