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Show that the Minimum Energy Needed to Separate a Proton from a Nucleus with Zprotons and N Neutrons is δ E = ( M Z − 1 , N + M B − M Z , N ) C 2 - Physics

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ConceptNuclear Energy Nuclear Fusion – Energy Generation in Stars

Question

Show that the minimum energy needed to separate a proton from a nucleus with Zprotons and N neutrons is `ΔE = (M_(Z-1,N) + M_B - M_(Z,N))c^2` 

where MZ,N = mass of an atom with Z protons and N neutrons in the nucleus and MB = mass of a hydrogen atom. This energy is known as proton-separation energy.

Solution

Given:
Mass of an atom with Z protons and N neutrons = MZ,N
Mass of hydrogen atom = MH
As hydrogen contains only protons, the reaction will be given by 

`E_(Z,N) → E_(Z-1,N) + p_1`

⇒ `E_(Z,N) → E_(Z-1,N) + ""^1H_1`

∴ Minimum energy needed to separate a proton, `ΔE = (M_(Z-1,N) + M_H - M_(Z,N))C^2`

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Solution Show that the Minimum Energy Needed to Separate a Proton from a Nucleus with Zprotons and N Neutrons is δ E = ( M Z − 1 , N + M B − M Z , N ) C 2 Concept: Nuclear Energy - Nuclear Fusion – Energy Generation in Stars.
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