Chapter 26 - Nuclear Physics Flashcards
what is Einstein’s mass-energy equation
E = mc^2
what are the main two ideas behind his mass-energy equation and give an example of each
1) Mass is a form of energy
- mass can be destroyed, releasing huge amounts of energy
- e.g. annihilation of an electron-positron pair into gamma photons
2) Energy has mass
- a change in energy of a system can lead to a change in mass of a system
- e.g. a tennis ball stationary weighs less than a moving one with K.E.
what can we say about the mass of the decay products of an alpha decay compared to the parent nuclei and what has happened to the lost mass
mass of the daughter nucleus and emitted particle < mass of the parent nucleus
- this is because energy is released when the particle is emitted
- this released energy has a mass equal to the difference in mass between the parent nucleus and the daughter nucleus/emitted particle
what occurs in annihilation
- when a particle and an antiparticle meet they completely destroy each other and all of their mass is converted to energy
- this energy is in the form of two very high energy photons
what are some minimum energies/energy changes for an electron-positron annihilation
change in mass = 2(Me)
change in energy = 2(Me)(c^2)
energy of a single photon = (Me)(c^2)
what occurs in pair production
- a high energy photon can disappear and form a particle and its respective antiparticle
why does a full nucleus weigh a different amount to the same number of protons/neutrons but separated
- when you separate nucleons, work must be done to overcome the strong nuclear force
- therefore the individual nucleons have a greater energy than the nucleus as a whole
- therefore they have a greater mass according to E = mc^2
define mass defect
“the mass defect of a nucleus is the difference in mass between the compete nucleus and the sum of the masses of the separate nucleons”
define binding energy
“the binding energy of a nucleus is defined as the MINIMUM energy required to completely separate a nucleus into its constituent nucleons”
how can we calculate binding energy from mass defect
binding energy = mass defect x c^2
is binding energy the same for all nuclei
no
how can we tell the stability of a nucleus
- calculate its binding energy per nucleon
how to calculate binding energy per nucleon
binding energy per nucleon = total binding energy / number of nucleons
what are the 4 main points we should remember about binding energy per nucleon and nucleon number
- for nuclei where A < 56, B.E. per nucleon increases with A
- for nuclei where A > 56, B.E. per nucleon decreases with A
- 56,26 Fe is the most stable nucleus
- 4,2 He, 12,6 C, and 16,8 O are have abnormally high B.E. per nucleon
how can we explain energy changes of spontaneous radioactive decay (alpha) in terms of binding energy
- binding energy of a parent nucleus < binding energy of daughter nucleus + alpha particle
- therefore energy is released as the kinetic energy of the alpha particle
how can we explain energy release of nuclear fusion in terms of binding energy
- two small (low mass/low A number) nuclei bond to form a bigger (higher mass/higher A number) nucleus
- given B.E. per nucleon increases with A for small nuclei, the total binding energy of the resultant nucleus is greater than the total binding energy of the individual nuclei
- therefore energy is released
how can we explain energy release of nuclear fission in terms of binding energy
- a big (high mass/high A number) nucleus splits into 2 smaller (lower mass/lower A number) nuclei
- given B.E. per nucleon increases when A decreases for a large nucleus, the total binding energy of the resultant nuclei is greater than the total binding energy of the parent nucleus
- so energy is released
how do we know where fission will occur in terms of nucleon number
- where A is large, fission will occur because binding energy per nucleon will increase when A decreases (nucleus splits)
- this means the products will be more energetically stable
how do we know where fusion will occur in terms of nucleon number
- where A is small, fusion will occur because binding energy per nucleon will increase when A increases (nuclei fuse)
- this means the product will be more energetically stable
what does fission involve and what is induced fission
- fission involves the splitting of a large nucleus into smaller daughter nuclei
- some isotopes split by themselves but many are induced by absorbing a neutron
what is the isotope generally used in fission reactors and what is used to induce its fission, which isotopes split spontaneously
Uranium - 235
U - 235
- we use ‘slow’ or thermal neutrons to induce fission as they will be absorbed by the nucleus making it unstable and causing it to undergo spontaneous fission
U-238 and U-235 rarely split spontaneously but U-236 does hence making U-235 absorb a neutron
what is the equation for nuclear fission, briefly explain what happens and how we can check it is correct
1,0 n + 235,92 U —> 236,92 U
—> 141,56 Ba + 92,36 Kr + 3(1,0 n)
- U-235 absorbs a slow neutron
- this makes it U-236
- this isotope is very unstable and breaks down into 3 fast neutrons and two daughter nuclei, Ba and Kr (or La and Br)
why is energy released in nuclear fission and how can we calculate this
- the mass of U-235 is higher than the mass of the daughter nuclei
- because the total binding energy of the daughter nuclei is higher than the total binding energy in U-235
- this missing mass/mass defect is released as energy in the form of kinetic energy
- we can use E=mc^2 to calculate it
what is the importance of chain reactions in nuclear fission and how can these be controlled
- the fission of U-235 produces 3 fast moving neutrons
- if these neutrons could be slowed then the reaction could be made into a chain reaction
- but the number of neutrons and therefore rate of reaction would grow exponentially if not controlled
- so control rods and moderators are used to help control this and prevent an uncontrolled reaction
- it is made so that on average, 1 of the 3 fast moving neutrons survives as a slow neutron
