Activity 1: Determining the value of aV

In this activity, you will determine the value for the volume (aV) term in the liquid drop model based on the experimental data for the isotopes of Oxygen (Z=8).

Semi-Empircal Mass Formula

Table 1 shows the parameters for the Liquid Drop (LD) formula. The sliders allow you to alter the constants. These changes will be reflected in Table 2. Note that the values for aS and aC are already given.

Table 2 shows the experimentally measured and theoretically calculated binding energy per nucleon for all observed isotopes of oxygen (Z=8). The theoretically calculated values use the liquid drop model and the parameters from Table 1.

Table 1: Constants of liquid drop formula (MeV)
Symbol Value
aV
aS 18.3
aC 0.714
aA
aP
Table 2
Number of Neutrons, N Number of nucleons, A BINDING ENERGY/(nucleon) (keV)
Experimental Theoretical Difference
5 13 5811.762
6 14 7052.301
7 15 7463.692
8 16 7976.206
9 17 7750.728
10 18 7767.097
11 19 7566.494
12 20 7568.57
13 21 7389.38
14 22 7364.858
15 23 7163.516
16 24 7039.685
17 25 6727.057

1(a) :: Oxygen-16 (A=16) has 8 protons and 8 neutrons. When an isotope has an equal number of protons and neutrons we say it is symmetric in Z and N. This means that the asymmetry term (aA) has no effect on the binding energy.

Oxygen-16 data is highlighted in Table 2 (above) as the green row.

Try changing the constant for the asymmetry term (aA) in Table 1 and convince yourself that the calculated (theoretical) binding energy for oxygen-16 (the green row in Table 2) has no dependency on the asymmetry term. Note that changing the constant will modify the binding energies of all of the other isotopes.

1(b) :: Since the asymmetry term does not affect the calculated binding energy for oxygen-16, we will use this to help us determine the volume term (aV).

We are aiming to change the parameters in Table 1 so that the differences in experimental and theoretical values are as close to zero as possible. This is called optimising the parameters.

Set aA = 0.

Modify the constant for the volume term (aV) in Table 1 until the difference between the model (theoretical) and measured data (experimental) for oxygen-16 (green row in Table 2) is close to zero. A reasonable range to start is between 10 and 20 MeV.

1(c) :: Leave your answer for aV in the Table to use for the next activity. You might also want to make a note of your value to discuss in the FutureLearn course.