Chemistry Practice Problems Mass Defect Practice Problems Solution: Which of the following nuclei is likely to have th...

Solution: Which of the following nuclei is likely to have the largest mass defect per nucleon: 11B, 51V, 118Sn, 243Cm?

Problem


A graph shows that binding energy increases rapidly, levels off, and then declines slowly.A graph shows that binding energy increases rapidly, levels off, and then declines slowly. The graph has mass number on the x-axis, ranging from 0 to 240 with intervals of 20, and binding energy per nucleon (10 to the minus twelfth power Joules) ranging from 0 to 1.4 with intervals of 0.2. Stability also increases up the y-axis (unscaled). Fusion (combining nuclei) releases energy at mass numbers below 56 (increases moving up left to right) and fission (splitting nuclei) releases energy at high mass numbers (increases right to left).


Which of the following nuclei is likely to have the largest mass defect per nucleon: 11B, 51V, 118Sn, 243Cm?

Solution

We’re being asked to determine which of the following nuclei is likely to have the largest mass defect per nucleon: 11B, 51V, 118Sn, 243Cm based on the plot of their binding energy.


To do so, we need to do the following steps,


Step 1: Based on the plot, determine the nucleon with the highest binding energy.
Step 2: Determine the nucleon with the largest mass defect (Δm) in kg, using the equation:


E=mc2

E = binding energy in J

Δm = mass defect in kg
c = speed of light = 3.0x108 m/s


Step 1: From the plot, we can see that the binding energy of each nucleon increases:


  • from left to right  → as mass numbers increase during fusion
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