Activity 4: Making predictions with the liquid drop model
Graph 3 (below) shows the experimentally measured and theoretically calculated binding energy per nucleon (BE/A) - as in Graph 1 previously - but extended to show mass numbers from 12 to 200. We are now using the liquid drop model to predict the binding energy per nucleon of oxygen isotopes with much higher masses than those experimentally observed (which have mass numbers of 13 to 25).
| Symbol | Value |
|---|---|
| aV | |
| aS | 18.3 |
| aC | 0.714 |
| aA | |
| aP | |
Using the liquid drop formula, we can calculate the heaviest isotope of oxygen with a positive binding energy. Anything heavier than this will not be bound, so cannot exist as a nucleus. This can be seen on the graph as the x-intercept going from a positive binding energy to a negative binding energy. The x-intercept is the number of nucleons shown below.
With the parameters you have entered, the heaviest isotope of oxygen predicted to exist will have a mass number, A, of 0 nucleons
What is the uncertainty in your prediction?
4(a) :: Assume that values of 20-25 MeV are possible for aA and that values of 15-17 MeV are possible for aV. Find the predicted range of mass numbers for the heaviest oxygen isotope with a positive binding energy.
The range of heaviest oxygen isotopes are from to nucleons.
You might also want to make a note of your value to discuss in the FutureLearn course.
4(b) :: Set your values of aA and aV back to your optimised values before progressing to the final activities.