Question

For Be-10, calculate (a) the mass defect. (b) the binding energy.

Short answer

Question: Calculate the mass defect and binding energy for Be-10 nucleus. Answer: The mass defect for Be-10 is 0.0089616 u, and the binding energy is 8.368 MeV.

Step-by-step solution

1. Determine the masses of the different particles involved

We must first find the mass of individual protons, neutrons and the actual mass of Be-10 nucleus. We can use the following values (in atomic mass units, u): - Mass of proton (m_p) = 1.007276 u - Mass of neutron (m_n) = 1.008665 u - Mass of Be-10 nucleus (m_Be) = 10.013534 u

2. Calculate the sum of individual nucleon masses

Next, we need to find the sum of the masses of the individual nucleons (protons and neutrons) in a Be-10 nucleus. As there are 4 protons and 6 neutrons, this can be calculated as follows: Sum of nucleon masses = (4 * m_p) + (6 * m_n) = (4 * 1.007276) + (6 * 1.008665) = 10.0224956 u

3. Calculate the mass defect

Now, we can find the mass defect as the difference between the sum of individual nucleon masses and the actual mass of the Be-10 nucleus: Mass defect = Sum of nucleon masses - m_Be = 10.0224956 - 10.013534 = 0.0089616 u (a) The mass defect for Be-10 is 0.0089616 u.

4. Convert mass defect to binding energy

Using Einstein's equation, E = mc^2, we can convert the mass defect into energy. First, we need to convert the mass defect to kilograms (1 u = 1.6605 x 10^-27 kg). Then, we'll use the speed of light, c = 3 x 10^8 m/s. Mass defect in kg = 0.0089616 u * 1.6605 x 10^-27 kg/u = 1.489 x 10^-29 kg Binding energy = (1.489 x 10^-29 kg) * (3 x 10^8 m/s)^2 = 1.341 x 10^-12 Joules To express the binding energy in a more convenient unit, we can convert it to mega-electronvolts (MeV) using the conversion 1 MeV = 1.602 x 10^-13 Joules. Binding energy in MeV = (1.341 x 10^-12 Joules) / (1.602 x 10^-13 Joules/MeV) = 8.368 MeV (b) The binding energy for Be-10 is 8.368 MeV.