## Question

The nuclear mass of 141ba is 140.883 amu. calculate the binding energy per nucleon for 141ba.

### Answer

**The final answer to the above question is 1.365392 x 10 ^{-12} Joules**

### Explanation

**Data**

The revealed pieces of information from the above question are:

Nuclear mass = 140.883 amu

Since the Barium atom can be written as ^{141}_{56}Ba

Thus,

The number of protons = 56 amu

Number of neutron = 141 – 56 = 85 amu

Hence to find the mass of both protons and neutrons, we will multiply their numbers by 1.00783 and 1.00867 respectively.

Thus,

Mass of protons = 1.00783 x 56 = 56.43848 amu

The mass of neutrons = 1.00867 x 85 = 85.73695 amu

#### Solution:

Now, to find the mass of a nucleon, we will use the equation below

**Mass of Nucleon = mass of proton + mass of the neutron**

Thus,

**Mass of Nucleon =** 56.43848 + 85.73695 = 142.17543 amu

We will now find the mass defect

**Mass Defect = Mass of Nucleon – Nuclear mass **= 142.17543 – 140.883 = **1.29243 amu**

The binding energy (BE) in MeV will now become

BE = 1.29243 x 931 MeV = 1203.25233 MeV

Since the question wants us to calculate the binding energy per nucleon for 141Ba, we will now say:

**The** **binding energy per nucleon for 141 Ba** = BE / 141 = (1203.25233) / 141 = 8.5337 MeV

We can further convert the above answer into joules by using **1 MeV = 1.6 x 10 ^{-13} J**

This implies that

**The** **binding energy per nucleon for 141 Ba** = 8.5337 MeV = 8.5337 x 1.6 x 10^{-13} J = 1.365392 x 10^{-12} J

**Therefore, the binding energy per nucleon of 141 Ba is 1.365392 x 10 ^{-12} Joules.**

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