Bunch of Nuclear Physics Question, Please help me.

Gigacore
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1. What fundamental force will decide the size of an atom?

still I've more to ask. . . waiting for reply
 
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There are following fundamental forces:

Gravitation: long distance force
electromagnetic force: Coulomb law
Weak force: is important in beta decay
Strong force: holds nucleons (proton, etc.) together

Since the electrons are kept near the nucleus because of the attractive Coulomb potential, the electromagnetic force decides the size of an atom.

However, in practice, this isn't just the influence of the electromagnetic force which decides the size of the atom. But it plays the leading role.
 
The problem here is what you mean when you say "size of atom". If you mean the effective size of an atom, it goes infinity because of coulomb force, and so coulomb force eleminate the other forces.
 
Of the 4 forces, the only one that matters is E&M - the others are too weak on the atomic scale. You can see this explicitly since the size of an atom is roughly of order the Bohr radius, which goes like 1/e^2 (so the weaker the charge, the larger the atom, as you might expect).
 
Toponium is a hadron which is the bound state of a valance top quark and a valance antitop quark. Oversimplified presentations often state that top quarks don't form hadrons, because they decay to bottom quarks extremely rapidly after they are created, leaving no time to form a hadron. And, the vast majority of the time, this is true. But, the lifetime of a top quark is only an average lifetime. Sometimes it decays faster and sometimes it decays slower. In the highly improbable case that...
I'm following this paper by Kitaev on SL(2,R) representations and I'm having a problem in the normalization of the continuous eigenfunctions (eqs. (67)-(70)), which satisfy \langle f_s | f_{s'} \rangle = \int_{0}^{1} \frac{2}{(1-u)^2} f_s(u)^* f_{s'}(u) \, du. \tag{67} The singular contribution of the integral arises at the endpoint u=1 of the integral, and in the limit u \to 1, the function f_s(u) takes on the form f_s(u) \approx a_s (1-u)^{1/2 + i s} + a_s^* (1-u)^{1/2 - i s}. \tag{70}...
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