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Solution: The nuclear masses of 7Be, 9Be, and 10Be are 7.0147, 9.0100, and 10.0113 amu, respectively.Which of these nuclei has the largest binding energy per nucleon?

Problem

The nuclear masses of 7Be, 9Be, and 10Be are 7.0147, 9.0100, and 10.0113 amu, respectively.

Which of these nuclei has the largest binding energy per nucleon?

Solution

We’re being asked to identify the nuclei with the largest binding energy per nucleon.


The binding energy is given by:

BE = m(c2)

where Δm = mass defect and c = speed of light


The mass defect of nuclei is given by:

m = theoretical mass - actual mass


The theoretical mass of nuclei is given by:

theoretical mass = Z(mp) + N(mn)

where 

Z is the number of proton

mp is the mass of a proton = 4.002604 amu

N is the number of neutron

mn is the mass of a neutron = 1.008665 amu


For each nuclei, we will do the following steps to calculate their binding energy then compare them:

Step 1: Calculate the theoretical mass

Step 2: Calculate the mass defect (Δm).
Step 3: Calculate the binding energy.
Step 4: Calculate the binding energy per nucleon.

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