Δ=(m(A,Z)-A)c^2, where m is the mass of the nucleus with atomic number Z and mass number A and he says that given Δ, we can use the nuclear binding energy to deduce the atomic mass, where the nuclear binding energy is: B=(Z×mH+N×mn-mA)c^2 , where mH is the mass of Hydrogen, mn is the mass of the neutron and mA the mass of the nucleus with atomic number Z, mass number A and N neutrons.

Slovenujozk

Slovenujozk

Answered question

2022-09-05

B = ( Z × m H + N × m n m A ) c 2 , where m H is the mass of Hydrogen, mn is the mass of the neutron and m A the mass of the nucleus with atomic number Z, mass number A and N neutrons.
What is the mass defect for real?

Answer & Explanation

madirans2m

madirans2m

Beginner2022-09-06Added 17 answers

First formula, Δ = ( m ( A , Z ) A ) c 2 is the binding energy, which is equal to μ c 2 , μ being the mass defect. Here, m ( A , Z ) is the observed mass of the nucleus, while Z m H + N m n Z m + ( A Z ) m = A m is the sum of masses of the nucleons making up the nucleus (and we assume that the proton and the neutron have equal mass m. For a stable nucleus, the above definition of Δ will be a negative quantity.
Yes, the two definitions are equivalent. The mass of a nucleus can be broken down into the two components: sum of masses of the constituent protons and neutrons, and the mass contributed by the binding energy ( μ = Δ / c 2 ).
m A = ( Z m H + N m n ) μ
The latter arises from the interaction between the protons and neutrons. The mass defect is precisely this second component of the mass.
If a nucleus (of mass m A ) were somehow dismantled completely into individual protons and neutrons (of mass m H , m n ), and we assumed (as in the case of breaking a large cube of wood into smaller wooden cubes) that the sum of masses of the constituents should be equal to the mass of the whole, we would find that our assumption was off, by an amount equal to the mass defect. From this, we conclude that the interaction that holds the protons and neutrons together (binding energy Δ) has to be included in the mass of the nucleus, making up the excess.

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