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

The nuclear mass of 37cl is 36.9566 amu. calculate the binding energy per nucleon for 37cl.
The nuclear mass of 37cl is 36.9566 amu. calculate the binding energy per nucleon for 37cl.

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.

You may also like to read:

Binding Energy: Definitions and Calculations

Reference:

St. Bonaventure University – Isotopes