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

## Question

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

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.

You may also like to read:

Binding Energy: Definitions and Calculations

## Reference:

St. Bonaventure University – Isotopes