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Question

If the charges of protons and neutrons is switched to negative and positive, will it affect the stability of atoms? justify

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Solution

The explanation can be as follows.

In an atom there are neutrons, protons and electrons as sub atomic particles.
Now, the main reason of stability of atom is the attractive/repulsive forces and the constant circulate motion of electrons in orbits.
In given case, if the charges are reversed keeping the positions same. That is all protons are at centre of electron bit with negative charge and all electrons in orbits with positive charges.
This is a hypothetical situation which is fixed on several factors. A proper answer can't be found without some sort of simulation or research. But even then I would list the following factors which can be considered.
- since we know that the magnitude of charge of electron and proton is same we can say that there won't be any difference in electrical forces.
- but importantly the mass of electron is negligible in comparison to that of proton.
- this may result in a different behaviour of these particles.
-there may be more of less force required to maintain the degeneracy of degenerate orbitals.

In nutshell we may say that the stability would not likely be affected if seen. But a research and experimentation is required to see the proper consequences.

I couldn't make it more particular. Hope it helps.

Hope it answers your question.
All the best!

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