The nuclear mass of 32S is 31.9633 amu. Calculate the binding energy per nucleon

Question

The nuclear mass of 32S is 31.9633 amu. Calculate the binding energy per nucleon for 32S. In this problem, to avoid rounding errors, use the constants Sapling gives you in the hint below, not the constants used in my notes. Also, be sure to use all decimal values provided.

The values of physical constants (such as the mass of a proton and the mass of a neutron) may be found here. The nuclear binding energy can be calculated using

DeltaE= c^2Deltam

where E is energy, ?m is the mass defect in kilograms, and c is the speed of light, 2.998 × 108 m/s.

mass of an electron me 9.10938291×10–28 g
5.4858×10–4 amu mass of a proton mp 1.672621777×10?24 g
1.007276467 amu mass of a neutron mn 1.674927351×10?24 g
1.008664916 amu

Explanation / Answer

The atomic number of S = 16

So, protons = 16

Mass number = 32

So, neutrons = 32-16 = 16

The mass of 1 proton is 1.007276467 amu
the mass of 1 neutron is 1.008664916 amu

So, mass of the nucleon is:

m=(16x1.00728)+(16x1.00866)=32.25504

the actual mass = 31.9633 amu.

Delta m = 32.25504 - 31.9633 amu.

= 0.2917 amu

0.2917 amu x (1.6605 x 10^-27 kg / 1 amu) = 4.844 x 10^-28 kg

The total binding energy E is calculated from

E = deltam x c^2

= (4.844 x 10^-28 kg)(2.998 x 10^8 m/s)^2

= 4.354 x 10^-11 J

Since there are 32 nucleons, so binding energy per nucleon

=(4.354 x 10^-11 J) / 32 nucleons

= 1.361 x 10^-12 J / nucleon

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