In chlorine, when the protons and electrons are equal, the charges cancel each other and the atom remains neutral. Then how does it accept one more electron when there is no force to act on it?

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Solution

This is because every atom try to completes its octet.In chlorine atom there are 7 electrons in its valence shell.According to *octet rule that needs one more electron to be stable.
Therefore it accepts one electron to acquire more stable state.
We needn't need a force for this.It is a law that every atom tries to completes its octet.Anyway you will learn more about this in higher classes and the concept will be more clear to you.

Octet rule:The octet rule is a chemical rule of thumb that reflects observation that atoms of main-group elements tend to combine in such a way that each atom has eight electrons in its valence shell, giving it the same electron configuration as a noble gas

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