Question

The mass of a proton is 1.00728 amu and that of a neutron is 1.00867 amu. what is the binding energy (in j) of a 61co nucleus? (the mass of a cobalt-61 nucleus is 60.9325amu.)

Answer 1

With the given equations the binding energy is $1.372 *10^{-12} J$.

How will you calculate binding energy using the given equations?

Step 1: The given data is:

The proton's mass 1.00728 amu

The neutron's mass 1.00867 amu

The mass of a cobalt-61 nucleus is 60.9325 amu

Step 2: Calculate binding energy

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

Mass of a cobalt61 nucleus = 60.9325 amu

Mass defect = Δm = 0.55884 u

ΔE =c²*Δm

ΔE = $(3.00 *10^8 m/s^2) *(0.55884 amu))*(1.00 g/ 6.02 *10^{23} amu)*(1kg/1000g)=8.36 * 10^{-11} J$

Step 3: Calculate binding energy per nucleon

ΔE $= 8.36* 10^{-11} J$

binding energy$= \frac{8.36* 10^{-11}}{60.9325} J = 1.372 *10^{-12} J$

The binding energy per nucleon $= 1.372 *10^{-12} J$

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