## 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 ^{37}_{17}Cl

Number of protons from ** ^{37}_{17}Cl (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 ** ^{37}_{17}Cl (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, M_{1} = 36.9566 u

**Unknown:**

Mass of Nucleon, M_{2} = ?

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 = M_{2} – M_{1}

And **Step 3:** Binding Energy = m / (number of nucleons)

### Solution

**Step 1**

Mass of the nucleon, M_{2} = mass of proton + mass of the neutron = 17.13311 + 20.1734 = 37.30651

**Step 2**

Mass Defect, m = M_{2} – M_{1} = 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