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

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

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

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

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 14156Ba

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

Reference:

Barium – University of Illinois