Answer :
With the given mass of proton and neutron, the binding energy is 1.372 * 10⁻¹² J.
How will you calculate binding energy using the given equations?
We are given data of proton's mass 1.00728 amu and neutron's mass 1.00867 amu. Also the mass of a cobalt-61 nucleus is 60.9325 amu
The mass defect = the difference between the mass of a nucleus and the total mass of its constituent particles.
Cobalt61 has 27 protons and 34 neutrons.
The mass of 27 protons = 27*1.00728 u = 27.19656 u
The mass of 34 neutrons = 34*1.00867 u = 34.29478 u
Total mass of protons + neutrons = 27.19656 u + 34.29478 u = 61.49134 u
Given Mass of a cobalt61 nucleus = 60.9325 u
Mass defect = Δm = Total mass- given mass=61.49134 u- 60.9325 u=0.55884 u
The difference in E is ΔE =c²*Δm. Putting the values we get,
ΔE = (3.00 *10⁸ m/s²) *(0.55884 amu))*(1.00 g/ 6.02 *10²³ amu)*(1kg/1000g)=8.36 * 10⁻¹¹ J
⇒ΔE =8.36 * 10⁻¹¹ J
Now binding energy=ΔE/given mass
=8.36 * 10⁻¹¹ /60.9325 J
=1.372 * 10⁻¹² J
The binding energy per nucleon 1.372 * 10⁻¹² J
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