🤓 Based on our data, we think this question is relevant for Professor Harman's class at UVA.

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

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

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

The **binding energy** is given by:

*$\overline{){\mathbf{BE}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{\u2206}}{\mathbf{m}}\mathbf{\left(}{\mathbf{c}}^{\mathbf{2}}\mathbf{\right)}}$*

where Δm = mass defect and c = speed of light

The **mass defect of nuclei** is given by:

*$\overline{){\mathbf{\u2206}}{\mathbf{m}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{theoretical}}{\mathbf{}}{\mathbf{mass}}{\mathbf{}}{\mathbf{-}}{\mathbf{}}{\mathbf{actual}}{\mathbf{}}{\mathbf{mass}}}$*

The **theoretical mass of nuclei** is given by:

$\overline{){\mathbf{theoretical}}{\mathbf{}}{\mathbf{mass}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{Z}}\mathbf{\left(}{\mathbf{m}}_{\mathbf{p}}\mathbf{\right)}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{N}}\mathbf{\left(}{\mathbf{m}}_{\mathbf{n}}\mathbf{\right)}}$

where

Z is the number of proton

m_{p} is the mass of a proton = 4.002604 amu

N is the number of neutron

m_{n} 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.