what force helps protons and neutrons to stay at the center of the atom?
In your own words, explain how Rutherford's theory of atoms helped in the development of the modern atomic theory.
Protons and neutrons (collectively called "nucleons") are held together by the strong nuclear force. And I mean "held together" in both senses. The strong force is responsible for binding the quarks that make up nucleons as well as binding the nucleons to each other to make a nucleus. I'm pretty sure Rutherford showed that atoms were composed of a 'cloud' of negative charge (electrons) surrounding a small, dense, positively-charged centre (the nucleus). Before that people thought atoms were composed of negative charges interspersed in some sort of positively charged material.
Rutherford model dismissed the Plum pudding model. http://en.wikipedia.org/wiki/Plum_pudding_model
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