Module 6: C26 - Nuclear Physics Flashcards
What is the Rest Mass on an object
The mass of an object, such as a particle, when it is stationary
What are the two interpretations of Einstein’s Mass-Energy equation E = mc^2
- Mass is a form of energy
- Energy has mass
What is the first interpretation of E = mc^2
The first interpretation is that mass is a form of energy.
The interaction of an electron-positron pair illustrates this idea well - the particles completely destroy each other (annihilation) and the entire mass of the parties is transformed into two gamma photons.
What is the second interpretation of E = mc^2
The second interpretation is that energy has mass.
The change of mass of an object, or a system, is related to the change in its energy, shown by ΔE = Δmc^2
A moving ball has kinetic energy, implying that its mass is greater than its rest mass. Similarly a decrease in the energy of system means the mass of the system must also decrease, like the mass of mug of hot tea will decrease as it cools and loses thermal energy.
Example Question:
Consider a person with rest mass 70 Kg sitting in a stationary car. Now imagine the car travelling at a steady speed of 15 ms-1. The person has gained kinetic energy, an increase in energy. The person will therefore have increased mass.
Calculate the change in mass.
ΔE = Δmc^2
Δm = ΔE/c^2
Δm = (1/2mv^2) / c^2
Δm = (1/2 x 70 x 15^2) / (3x10^8)^2
Δm = 8.8x10^-14 kg
In natural radioactive decay, why is the mass of the daughter nucleus and alpha particle less than the original parent nucleus.
As energy is released in radioactive decay, a decrease in mass has to take place too.
This means the total mass of the alpha particle and daughter nucleus must be less than the mass of the parent nucleus.
This decrease in mass Δm is equivalent to the energy released ΔE
Example Question:
Positrons are the antiparticles of electrons. When they meet, they annihilate each other, and their entire mass is transformed into energy in the form of two identical gamma photons. Calculate the minimum energy of each photon.
Mass of electron/positron = 9.11x10^-31
E = mc^2
E = [(2 x 9.11x10^-31) x (3x10^8)^2] / 2 = 8.199x10^-14
What is Pair Production
Pair production is the replacement of a single
photon with a particle and a corresponding
antiparticle of the same total energy.
When two protons collide is the total rest mass higher before or after the collision
p + p —> p + n + π^+
The total rest mass of the particles after the collision is greater than before. The increase Δm multiplied by c^2 must be equal to the minimum kinetic energy of the colliding protons.
Example Question:
Mass of a deuterium nucleus = 2.013553 u
Mass of proton = 1.007276 u
Mass of neutron = 1.008665 u
Mass of electron = 0.00055 u
a) What is difference between a mass of a deuterium and separated proton and neutron.
b) Calculate the energy equivalent of a deuterium nucleus.
c) Calculate the total energy equivalent of a proton and a neutron.
a)
Sum of parts : 2.016491 u
Mass: 2.013553 u
Difference: 2.388x10^-3 u
b)
E = mc^2
2.01355 x 1.661x10^-27 = 3.345x10^-27
E = (3.345x10^-27) x (3x10^8)^2
E = 3.01006x10^-10 J
c)
1.007276u + 1.008665u = 2. 015941u
2.015941 x 1.661x10^-27 = 3.348x10^-27
3.348x10^-27 x (3x10^8)^2 = 3.01363021x10^-10 J
What is Mass Defect
The mass defect of a nucleus is defined as the difference between the mass of the completely separated nucleons and the mass of the nucleus.
What is Binding Energy
The binding energy is the minimum energy required to completely separate a nucleus into its constituent protons and neutrons.
What is the Binding Energy per nucleon
Binding energy per nucleon is a more useful quantity as it compares the binding energy to the number of nucleons in an atom.
The mass of a uranium-235 (nucleon number: 235, proton number:92) nucleus is 235.004393u.
Calculate its binding energy in MeV.
Step 1: Calculate the total mass of the constituent nucelons.
The uranium-235 nucleus has 92 protons and (235-92) = 143 neutrons.
Therefore, mass of nucleons = (92x1.007276) + (143 x 1.008665) = 236.908487 u
Step 2: Calculate the mass defect for the uranium-235 nucleus.
Mass defect = 235.004393 - 236.908487 = (-)1.904094u
Step 3: Change the mass defect from u to kg
(1u = 1.661x10^-27 kg)
Mass defect = 1.904094 x 1.661x10^-27 = 3.162x10^-27 kg.
Step 4: Calculate the binding energy and convert it from J to eV using the conversion factor 1eV = 1.60x10^-19 J
Binding energy = mass defect x c^2
Binding energy = 3.162x10^-27 x (3.0x10^8)^2 = 2.84x10^-10 J
Binding energy = 2.84x10^-10 / 1.60x10^-19 = 1.779x10^9 eV
Binding energy = 1780 MeV
What does the binding energy per nucleon say about how stable the nucleus is
The greater the binding energy (BE) per nucleon, the more tightly bound the nucleons within the nucleus are, or in the other words a nucleus is more stable if it has greater BE per nucleon.
What element nucleus has the greatest (Binding Energy) per nucleon?
The nucleus of iron-56 (Fe) has the greatest BE per nucleon - it is the most stable isotope in nature
What is Induced Fission
Nuclear fission occurring when a nucleus becomes unstable on absorbing another particle (such as a neutron)
What is a thermal neutron
A neutron in a fission reactor with mean kinetic energy similar to the thermal energy of particles in the reactor core - also known as a slow neutron.
What is a typical induced fission reaction of uranium-235 by a thermal neutron
¹₀n + ²³⁵₉₂U —> ²³⁶₉₂U —> ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3 ¹₀n
Describe the process of a typical induced fission reaction of uranium-235 by a thermal neutron
The uranium-235 nucleus captures a thermal neutron and becomes a highly unstable nucleus or uranium-236. In less than a microsecond, the uranium-236 nucleus splits. The daughter nuclei produced in this example are barium-141 and krypton-92. Three fast neutrons are also produced. The equation is balanced as the number of protons and nucleons are conserved
How is energy emitted from nuclear fission
The total binding energy of the particles after fission is greater than the total binding energy before it. The difference in binding energies is equal to the energy released.
The energy released in a single fission reaction is a combination of kinetic energy if the particles produced and the energy of photons and neutrinos emitted.
Explain how nuclear fission can provide energy
It can provide energy, as the uranium becomes unstable with the extra neutron and will split up into two other elements and fast neutrons. Energy is also produced in this reaction, as the mass of the system decreases (E=mc^2)
Worked example: Energy from fission
The difference in mass in the induced fission of uranium-235 is about 0.185u.
Calculate the total energy released in this reaction in MeV.
Step 1: Change Δm from u to kg (1u = 1.661x10^-27kg).
Δm = 0.185 x 1.661x10^-27 = 3.07x10^-28 kg
Step 2: Use Einstein’s mass-energy equation to calculate the energy released
Energy released ΔE = mc^2
ΔE = 3.07x10^-28 x (3.00x10^8)^2 = 2.76x10^-11J
Step 3: Change the energy from joules to electron volts
(1eV = 1.60x10^-19J)
ΔE = 2.76x10^-11/1.6x10^-19 = 172.5x10^6 eV = 170MeV
What might happen if the three fast neutrons produced in a fission reaction are slowed down
A chain reaction becomes possible, with these three neutrons starting three more reactions, which each produce another three neutrons, and so on.
