Question
The nuclear mass of 37cl is 36.9566 amu. calculate the binding energy per nucleon for 37cl.
Answer
The final answer to the above question is 1.4087187 x 10-12 Joules
Explanation
Data: Revealed information from the question
From the chlorine element 3717Cl
Number of protons from 3717Cl (Superscript) = 17
We can now multiply 17 by the mass of protons [Note: mass of proton = constant = 1.00783]
Mass of the protons = 17 x 1.00783 = 17.13311 u
The number of Neutrons 3717Cl (Subscript) = 37
Hence, multiply 37 by the mass of neutrons [Note: mass of neutron = constant = 1.00867]
Mass of the Neutrons = 37 x 1.00867 = 20.1734 u
Mass of the Nucleus, M1 = 36.9566 u
Unknown:
Mass of Nucleon, M2 = ?
Mass Defect, m = ?
Binding Energy, E = ?
Formula
Step 1: Mass of Nucleon = mass of proton + mass of the neutron
The second Step 2: Mass Defect, m = M2 – M1
And Step 3: Binding Energy = m / (number of nucleons)
Solution
Step 1
Mass of the nucleon, M2 = mass of proton + mass of the neutron = 17.13311 + 20.1734 = 37.30651
Step 2
Mass Defect, m = M2 – M1 = 37.30651 – 36.9566 = 0.34991 u
To convert mass defect into MeV, we will say
m = 0.34991 x 931 MeV = 325.76621 MeV
We will now convert the above expression into joules. Considering the fact that 1 MeV = 1.6 x 10-13 J, we will now have:
m = 325.76621 x 1.6 x 10-13 J = 5.21225936 x 10-11 J
Step 3
Binding Energy = m / (number of nucleons) = (5.21225936 x 10-11) / 37 = 1.4087187 x 10-12 J
We can now approximate the above answer into 1.4 x 10-12 Joules
Therefore, the final answer which is the binding energy per nucleon of 37-Chlorine (37cl) is 1.4087187 x 10-12 Joules which can be approximated into 1.4 x 10-12 Joules.
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Binding Energy: Definitions and Calculations
