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# Find the Binding Energy per Nucleon of 197 79 Au If Its Atomic Mass is 196.96 U. - Physics

ConceptMass-energy and Nuclear Binding Energy Nuclear Binding Energy

#### Question

Find the binding energy per nucleon of ""_79^197"Au" if its atomic mass is 196.96 u.

(Use Mass of proton mp = 1.007276 u, Mass of ""_1^1"H" atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)

#### Solution

Given:-

Atomic mass of Au, A = 196.96
Atomic number of Au, Z = 79
Number of neutrons, N = 118
Binding energy,

B = (Zm_p + Nm_n - M)c^2

Here, mp = Mass of proton
M = Mass of nucleus
mn = Mass of neutron
c = Speed of light

On substituting the respective values, we get

B = [(79 xx 1.007276 + 118 xx 1.008665) "u" - 196.96  "u" ] c^2

= (198.597274 - 196.96) xx 931  "MeV"

= 1524.302094  "MeV"

Binding energy per nucleon = 1524.3/197 = 7.737  "MeV"

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Solution Find the Binding Energy per Nucleon of 197 79 Au If Its Atomic Mass is 196.96 U. Concept: Mass-energy and Nuclear Binding Energy - Nuclear Binding Energy.
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