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The Hydrogen-1 isotope is a form of hydrogen with 1 electron, 1 proton, and 0 neutrons. If that isotope were to lose its electron (thus being a Hydrogen-1 ion with a positive charge) what would be the different between it and a free proton? The positive Hydrogen-1 would contain 0 electrons, 1 proton, and 0 neutrons and the free proton would obviously contain only 1 proton. Is there a defining factor that would distinguish between a free proton and positive Hydrogen-1 ion?

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They are the same. – jinawee Jan 27 '14 at 0:42 there a defining factor?... No. A proton is a proton is an H+ ion. – james large Dec 29 '15 at 16:26
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The diameter of nuclei of Hydrogen atom is in the range of $1.75$ fm. You might think that, the proton lies inside this boundary in case of positive hydrogen-1 ion and the free proton doesn't have any definite boundary. It is not the case, the diameter of the nuclei of hydrogen atom is nothing but the diameter of the proton. So, there is no difference between positive hydrogen-1 ion and a free proton.

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  1. In the NEBULA, ionized hydrogen gas in plasma in free space has the electrons freed to higher orbits and emits radiations as follows: Lyman series (n′ = 1); Balmer series (n′ = 2); Paschen series ( n' = 3); Brackett series (n′ = 4); Pfund series (n′ = 5).
  2. ELECTROLYTES IN SOLUTION: Ionized cation hydrogen in liquid with hydroxil anions are present.
  3. COSMIC RAYS: Q: Is free proton same as H+ ion? Answer: No. Free protons are present in high energy cosmic rays, and they tend to form an electron shell in the instant the energy level comes down.
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