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5.3.4 Nuclear Fission and Fusion. (a) select and use Einstein’s mass–energy equation Δ E = Δ mc 2. Introduction and background. All nuclei want to be (more) stable. Introduction and background.
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(a) select and use Einstein’s mass–energy equation ΔE = Δmc2
Introduction and background All nuclei want to be (more) stable
Introduction and background • Elements with a proton (atomic) number greater than 83 are unstable in the sense that they decay naturally. • They do so through radioactive emission. • There is a way of causing some of the larger nuclei, 238U and 239Pu each with 92 and 94 protons respectively, to split apart into two more stable fragments, forming new nuclei. • This is known as Nuclear Fission.
Nuclear fission We induce fission through neutron collision. The neutron is initially absorbed by the nucleus it collides with. This makes it more unstable and it therefore breaks apart often releasing several neutrons which can go on to cause further nuclei to split. Note – Charge is conserved
Fusion • All nuclei want to be (more) stable • Nuclei of very low mass can also become more stable by joining together to make more massive nuclei. H + H He H + H H + H 2 1 3 1 1 2 1 3 2 2 1 1 1 1
Where does the energy come from? • Nucleons are held together by the strong, nuclear force. • To remove a nucleon from a nucleus, work has to be done against this attractive force. As work is done, the potential energy of the nucleon increases. This is similar to doing work against gravity. • The total energy required or work done is said to be the binding energy of the nucleon. In other words, the energy by which it was originally bound to the nucleus.
Where does the energy come from? • The lower the potential energy of a nucleus, the greater its binding energy. Similarly the lower a rocket is in the Earth’s gravitational field, the greater the energy needed in order for it to escape. • Nuclear interactions do not obey ‘normal’, (classical mechanics), laws of conservation of energy and mass as it is possible for energy to be converted into mass and vice-versa.
Einstein’s mass-energy equation E = mc2 where E = Energy (J) m = Mass (kg) c = Speed of light (ms-1)
Example 1 Particles A and B interact to make particles C and D. A + B C + D If the measured mass of A added to that of B is greater than the measured mass of C added to that of D; mA + mB > mC + mD then the missing mass on the right hand side turned into energy in the interaction and was released.
Example 1 • The energy released also represents the overall increase in the binding energy of the two new particles.
Example 2 Particles A and B interact to make particles C and D. A + B C + D If the measured mass of A added to that of B is less than the measured mass of C added to that of D; mA + mB < mC + mD then the missing mass on the left hand side is the energy required to make the interaction take place.
Example 2 • This ‘missing mass’ or ‘mass deficit’ in nuclear interactions allows us to determine either the energy released or required by an interaction
How is this calculated? E = mc2 Where; E = Energy (J) m = ‘deficit’ or ‘missing’ Mass (kg) c = Speed of light (ms-1)
Units • Use (kg) and (J) in E = mc2 • However, as the energy released during nuclear reactions or processes is so small, it is often quoted in eV. • 1eV ≡ 1.6×10-19J • It is similar with the masses involved. They are often quoted in unified atomic mass units. Carbon 12 has a mass of 12u • 1u ≡ 1.661×10-27kg
Units As mass and energy are interchangeable on this level we can say that; 1u ≡ 1.66×10-27kg ≡ 931MeV ≡ 1.49×10-10J
Worked Example 2 2 3 1 H + H He + n + energy Measured mass of H = 2.015u Measured mass of LHS = 2 x 2.015u = 4.030u Measured mass of He = 3.017u and n = 1.009u Measured mass of RHS = 4.026u RHS mass deficit of 0.004u, therefore 3.7MeV of energy produced in this interaction. 1 1 2 0
Question DATA; all masses are measured. He = 4.001506u, p = 1.007276u, n = 1.008665u a.) Calculate the energy (in eV and J) released when an alpha particle is constructed. b.) Does this represent the binding energy of an alpha particle? 4 1 1 2 0 1
Answers a.) 28.3MeV and 4.53x10-12J b.) Yes
Mass deficit • The Binding energy of any nucleus can be calculated in the same way. The ‘missing mass’, the difference between the mass of the nucleus and that of the ‘free’ nucleons is called the mass deficit.
Binding energy per nucleon • If we divide the binding energy of a nucleus by the number of nucleons it contains, we have calculated the average binding energy per nucleon B. • A graph of B against nucleon number is one of the most important in nuclear physics.
