Flashcards in Nuclear Physics Deck (60):
Describe the Rutherford scattering experiment
-Investigate the scattering of alpha particles by a thin foil of gold, and an Alpha source placed in long thin lead container to produce a well-directed beam of alpha particle, gold foil and the whole apparatus was evacuated so that the alpha particles could travel without being stopped by air
1. Over a period of months, Geiger and Marsden counted the number of alpha particles deflected at different angles theta
2. The alpha particles were detected by a f;uorecent screen and each time an alpha particle hit the screen a small flash of light was emitted which was seen through a microscope and they counted hundreds of thousands of such flashes of light
3. The vast majority of the alpha particles were detected through large angles of about 150 degrees or more
What were the conclusions of the Rutherford scattering experiment?
1. The atom has a very small positively charged. nucleus and Rutherford suggested that the positive charge on the nucleus is responsible for the repulsive force on the positively charged alpha particle, which causes it to change direction. The fact that only a very small number of particles undergo a large deflection tells us that the nucleus is much smaller in diameter than the atom
2. The nucleus contains nearly all the mass of the atom and consideration of the conservation of momentum tells us that the alpha particle would knock a small cells out of the way but that the alpha particle will bounce back after an encounter with a nucleus much heavier than itself
-Using our knowledge of electrostatic theory it is possible to calculate the maximum size of the gold nucleus. If an alpha particle is tuned round by 180 degrees, it much have encountered a gold nucleus head on and there must have been a moment when the alpha particle stopped moving, Then all of the alpha particle's kinetic energy has been transferred to electrical potential energy
What is a femtometer?
Nucelar radii and diameters are measured in femtometers, 10-15. The unit is abbreviated to fm
How do you figure out the momentum of electrons?
p = E (electron energy) / c (speed of light)
How do you calculate the wavelength of the electrons?
lamda = h (planck constant) / p (the electron's momentum)
How do you calculate the diameter of the nucleus?
sin theta (angle of the first diffraction minimum) = 1.22 lamda (wavelength of the light) /d (diameter of the particles)
What is the empirical formula of the radius of a nucleus?
What does empirical mean?
The equation is based purely on experimental results. it is not exact but it gives an approximate value for a nuclear radius
What is an atomic mass unit?
One atomic mass unit (1u) is equal to 1.67 x 10-27 kg
What is a becquerel?
The activity of a radioactive source is equal to the number of particles emitted per second. the unit of activity is the becquerel (Bq). 1 becquerel (1Bq) = an emission of one particle per second
Describe alpha particles
1. Helium nucleus: 2 protons and 2 neutrons
2. Mass: 4u , 6.6 x 10 -27 kg
3. Charge: +2e
4. Strongly ionising
5. Travel few centimetres in air and can be stopped by a sheet of paper
6. Deflected slightly in strong electric and magnetic fields
7. Speed: 5% of c
Describe beta particles
1. Fast electron
2. Mass: 9.1 x 10-37 kg
3. Charge: -e
4. Less ionising than alpa
5. Travel several meters in air and can be stopped by a few mm of lead
6. Significant deflection in electric and magnetic fields
7. Speed: 98-99% of c
Describe gamma rays
1. Electromagnetic photon
2. 0 mass and charge
3. Very weakly ionising and very penetrating, few centimetres of lead
4. No deflection in electric and magnetic fields as not charged
5. Speed: c
What did scientists think before the scattering?
-Scientists thought that atoms were like a plum pudding
1. The idea of atoms has been around since the time of the Ancient Greeks in the nth Century BC. Democritus proposed that all matter was made up of little, identical lumps called 'atomos'
2. Much alter, in 1804, John Dalton put froward a hypothesis that agreed with Democritus - that matter was made up of tiny spheres ('atoms') that couldn't be broken up. He reckoned that each element was made up of a different type of 'atom'
3. Nearly 100 years later J.J Thomson discovered that electrons could be removed from atoms. So Dalton's theory was not quite right (atoms could be broken up)
4. Thomson suggested that atoms were spheres of positive charge with tiny negative electrons stuck in them like fruit in a plum pudding
5. Until this point though nobody had proposed the idea of the nucleus. Rutherford was the first to suggest atoms did not have uniformly distributed charge and density
How did Rutherford's scattering show the existence of a nucleus?
1. In 1909, Rutherford and Marsden tried firing a beam of alpha particles at thin gold foil
2. A circular detector screen surrounding the gold foil and the alpha sources was used to detect alpha particles deflected by any angle
3. They expected that the positively charged alpha particles would be deflected by the electrons by a very small amount if the plum pudding model was true
4. Instead most of the alpha particles went straight though the foil, while a small number were deflected by a large angle
5. Some were even deflected by more than 90 degrees, sending then back the way they came - this was confusing at the time and called for a change to the model of the atom
What did the results of the Rutherford scattering model suggest?
-That atoms must have a small, positively charged nucleus at the centre;
1. Most of the atom must be empty space because most of the alpha particles passed straight though the foil
2. The nucleus must have a large positive charge, as some positively-charged alpha particles were repelled and deflected by a large angle
3. The nucleus must be very small as very few alpha particles were deflected back
4. Most of the mass must be in the nucleus, since the fast alpha particles (with high momentum) are deflected by the nucleus
How can you estimate the closet approach of a scattered particle?
1. When you fire an alpha particle at a gold nucleus, you know tis initial kinetic energy
2. An alpha particle that 'bounces back' and is deflected through 180 degrees will have revered direction a short distance from the nucleus. It does tis at the point where its electric potential energy equals its initial kinetic energy
3. It is just conservation fo energy and you can use it to find how close the particle can get to the nucleus (NOTES)
5. To find the charge of a nucleus you need to know the atom's proton number, Z that tells you how many protons are in the nucleus. A proton has a charge of +e (where e is the size of the charge on an electron), so the change of a nucleus must be +Ze
6. The distance of closet approach is an estimate of nuclear radius - it gives a maximum value for it. However, electrons diffraction gives much more accurate values for nuclear radii
How can you use electron diffraction to estimate nuclear radius?
1. Electrons are a type of particles called lepton. Leptons do not interact with the strong nuclear force (whereas neutron and alpha particles do). Because of this, electron diffraction is an accurate method for estimating the nuclear radius
2. Like other particles, electrons show wave-particle duality, she electron beams can be diffracted
3. A beam of moving electrons has an associated de Broglie wavelength, lamda, which at high speeds (where you have to take into account relativistic effects is approximately lamda = hc/E
4. The wavelength must be tiny (around 10^-15m) to investigate the nuclear radius, so the electrons will have to have a very high energy
5. If a beam, of high energy electrons is directed onto a thin film of material in front of a screen, a diffraction pattern will be seen on the screen
6. The first minimum appeared where sin theta = 1.22lamda / 2R
7. Using measurements from this diffraction pattern you can rearrange the above equation to dine the radius of the nucleus
How does intensity vary?
-Intensity varies with diffraction angle
1. The diffraction pattern is very similar to that of a light source shining through a circular aperture - a central bright maximum (circle) construing the majority of the incident electrons, surround by other dimmer rings (maxima)
2. The inentisity of the maxima decreases as the angel of diffraction increases. The graph shows the relative intensity of electrons in each maximum
-You might see a logarithmic plot of this graph where the different in the peak heights is less pronounced
What is the nuclear radius like in comparison to the atomic radius?
-The nuclear radius is very small in comparison to the atomic radius
-By probing atoms using scattering and diffraction methods, we know thatL
1. The radius of na atom is about 0.05nm (5 x 10^-11)
2. Te radius of the smallest nucleus is amount 1fm (1 x 10^-15
-So nuclei are really tiny compared with the size of the whole atom
What is the typical radius of a nucleus?
1 x 10^-15m
What is the nucleus made up of?
-The nucleus is made up of nucleons
1. The particles that make up the nucleus ( protons and neutrons) are known as nucleons
2. The number of nucleons in an atoms is called the nucleon (or mass) number, A
3. As more nucleons are added tot he nucleus, to gets bigger
4. You na measure the size of. nucleus by firing particles at it
What is the nuclear radius proportional to?
-Nuclear radius is proportional tot he cube root of the nucleon number
1. When data from nuclear radii experiment is plotted on a graph of nuclear radius R against the cube root of the nucleus number A^1/3, the line of best fit gives a straight line
2. This shows a linear relationship between R and A^1/3 . As the nucleon number increase, the radius of the nuclear increases proportionally to the cube root of A
3. R=R0A^1/3 where R0 is roughly 1.4 fm
Whta is the density of nuclear matter like?
-The density of nuclear matter is enormous
1. The volume that each nucleon (i.e. a proton or a neutron) rakes up in a nucleus is about the same
2. Because protons and neutrons have nearly the same mass (we'll call it mnucleon) it means that all nuclei have a similar density (rho), which you can quickly prove
3. If you substitute the instant into this formula, you'll get that the nuclear density is run 1.45 x 10^17 kgm^-3
4. Nuclear matter is no ordinary stuff. Its density is enormous, much larger than atomic density. This suggests that an atom contains lots of empty space, with most of its mass being in a small nucleus
What are unstable nuclei like?
-Unstable nuclei are radioactive
1. If a nucleus is unstable, it will break down to become more stable. Its instability could be cause dry having too many neutrons, no enough neutrons or just too much energy in the nucleus
2. The nucleus decays by releasing energy and/or particles until it reaches a stable form, this is called radioactive decay
3. When a radioactive particle hits an atom it can knock off electrons, creating an ion - so, radioactive emissions are also known as ionising radiation
4. An individual radioactive decay is random - it cannot be predicted
How can you use penetrating power to investigate radiation types?
-Different types of radiation have different penetrate power, and so can be stopped by different types of material:
1. Record the background radiation count rate when no source is present
2. Place an unknown source near to a Geiger counter and record the count rate
3. Place a sheet of paper between the source and the Geiger counter, record the count rate
4. repeat step 2, replacing the sorer with a 3mm thick sheet of aluminium
-Depending on whether the count rate significantly decrease, you can collate what kind of radiation the source was emitting. For example, if paper has no effect and aluminium cause a significant (but not complete) reduction n count rate, the source must be emitting beta and gamma radiation
How can you control how thick material is using radiation?
1. When creating sheets of material, like paper foil or steel, ionising radiation can be sued to control its thickness
2. The material is flatted as it is fed through rollers
3. A radioactive source is placed on one side of the material, and a radioactive detector on the other. The thicker the material, the more radiation art absorbs and prevents from reaching the detector
4. If too much radiation is absorbed, the rollers move closer together to make the material thinner. if too little ration is being absorbed, they move further apart
Describe the different ionising properties of alpha and beta particles
-What a radioactive source can be used for often depends on its ionising properties
1. Alpha particles are strongly positive, and so they can easily pull electrons off atoms
2. Ionising an atom transfers some of the energy from the alpha particle to the atom. The alpha particle quickly ionises many atoms (about 10,000 ionisation our mm in air for each alpha particles) and loses all its energy. This makes alpha-sources suitable for use in smoke alarms because they allow current to flow. but won't travel very far
3. Although alpha particles can't penetrate your skin, sources of alpha particles are dangerous if they are ingested, They quickly ionise body tissue in a small area, causing lots of damage
4. The beta-minus particle has a lower mass and change than the alpha particle, but. higher speed, Tis means it can still knock electrons off atoms. Each beta particle will ionise about 100 atoms per mm in air, losing energy at each interaction
5. This lower number of interactions means that beta radiation causes much less damage to body tissues
6. Beta radiation is commonly used for controlling the thickness of a material
How are gamma rays used in medicine?
-Gamma radiation is even more weakly ionising that beta radiation, so will do even less damage to body tissue. This means that it can be sued in medicine:
1. Radioactive tracers ar eisend to help diagnose patients without the need for surrey. A radioactive source with a short half-life to revert prolonged radiation exposure is either eaten or injected into the patient. A detector, e.g. a PET scanner, it then used to detect the emitted gamma rays
2. Gamma rays can be used in the treatment of cancerous tumours - damaging cells and sometimes curing patients of cancer. Radiation damages all cells, cancerous or not and so sometimes a rotating beam of gamma rays is used. This lessens the damage done to the surrounding tissues, whilst giving a high does of radiation to the tumour at the centre of radiation
3. Damage to other, healthy cells is not completely prevented however and treatment can cause patients to suffer side effects - such as tiredness and reddening or soreness of the skin
4. Exposure to gamma radiation can also cause long term side effects like infertility for certain treatments
5. As well as patients, the risks towards medical staff giving these treatments mist be kept as low as possible. Exposure time to radioactive sources is kept to a minimum, and generally staff leave the room (which is itself shielded) during treatment.
-Simply put, radiation use in medicine has benefits and risks. The key is trying to use methods which reduce the risk (shielding, rotating beams etc.) while giving you the results you want. It's all one big balancing act
How do you detect background radiation?
-Put a Geiger counter anywhere and the counter will click, it is detecting background radiation
-When you are a reading from a radioactive source, you need to measure the background radiation separately and subtract it from your measurement
What are the different sources of background radiation? Describe them
1. The air
2. The ground and buildings
3. Cosmic radiation
4. Living things
5. Man-made radiation
What is the air's background radiation?
-Radioactive radon gas is released from rocks
-It emits alpha radiation
-The concentration of this gas in the atmosphere varies a lot from place to alcove, but it is usually the largest contributor to background radiation
What are the ground and building background radiation?
-All rock contains radioactive isotopes
What is cosmic radiation background radiation?
-Cosmic rays are particles (mostly high-energy protons) from space
-When they collide with particles in the upper atmosphere, they produce nuclear radiation
What are living thing's background radiation?
-All plants and animals contain carbon, and some of this will be radioactive carbon-14
-They also contain other radioactive material such as potassium-40
What are mad made background radiation?
-In most areas, radiation from medical or industrial source makes up a tiny, tiny fraction of the background radiation
What does the intensity of gamma radiation obey?
-The intensity of gamma radiation obeys the inverse square law
1. A gamma source will emit gamma radiation in all directions
2. This radiation spreads out as you get further away from the source
3. This means the amount of radiation per unit area (the intensity) will decrease the further you get form the source
4. If you took a reading of intensity, I at a distance x from the source you find that it decrease but eh square of the distance from the source
-This can be written as the equation I=k/x^2
where k is a constant
5. This relationship can be proved by taking measurements of intensity at different distances from a gamma source, using a Geiger counter
6, If the distance form the source is doubled, the intensity is down to fall to a quarter which verifies the inverse square law
How do you consider the inverse square law when working with radioactive sources?
1. Using a radioactive source becomes significantly more dangerous the closer you get to the source. This is why you should always hod a source away from your body when transporting it through the lab
2. Long handling tongs should also be used to minimise the radiation absorbed by the body
3. for those not working directly with radioactive source, it is best to just keep as far away as possible
How can you investigate the inverse square law?
1. Set up the equipment as shown in the diagram, leaving out the source at first (DIAGRAM)
2. Turn on the Geiger counter and take a reading of the background radiation count rate (in counts per sec). Do this three times and take an average
3. Place the tube of the Geiger counter so it is lined up with start of the rule
4. Carefully place the radioactive source at a distance d from the tube
5. Record the count rate at that distance. Do this 3 times and take an average
6. Move the source so the distance between it and the Geiger counter doubles (2d)
7. Repeat steps 5 and 6 for distances of 3d, 4d etc.
8. Once the experiment is finished, put away your source immediately - you don't want to be exposed to more radiation than you need to be
9. Correct your data for background radiation and then plot a graph of corrected count rate against durance of the counter from the source, You shoulder that as the distance doubles, the corrected count rate drops to a quarter of its starting value, supporting the inverse square law
How does every isotope decay?
-Every isotope decays at a different rate
1. Radioactive decay is completely random. You can't predict which atom's nucleus will decay when
2. Although you can't predict the decay of an individual nucleus, if you take a very large number of nuclei, their overall behaviour shows a pattern
3. Any sample of a particle isotope has the same rate of decay, i.e. the same proportion of atomic nuclei will decay in a given time
-Isotopes of an element have the same number of protons, but different number of neutrons in their nuclei
How is the rate of decay measured?
-The rate of decay is measured by the decay constant
1. The activity of a sample, the number of nuclei (N) that decay each second, is proportional to the size of the sample
2. For a given isotope, a sample twice as big would give twice the number of decays per second
3. Activity is measured in Bequerels (Bq) and 1 Bq = 1 decay per second
-The number of radioactive nuclei decaying per second (activity) is proportional to the number of nuclei remaining
What is the decay constant?
The decay constant (lamda) is the probability of a given nucleus decaying per second, the bigger the value of lamda, the faster the rate of decay, its unit is s^-1
What is the definition of half-life?
The half like (T1/2) of an isotope is the average time it takes for the number of unstable nuclei to halve
-Measuring the number of unstable nuclei isn't the easiest job in the world and in practice, half-life isn't measured by counting nuclei, but by measuring the time it takes the activity to halve, The longer the half-life of an isotope, the linter it stays radioactive
What is the equation for half life?
T1/2 = ln2 / lamda = 0.693 / lamda
How do you figure out the number of unstable nuclei remaining?
-The number of unstable nuclei remaining N depends on the number originally present, N0 and the number remains can be calculated:
N=N0e^-lamdat (t is time in seconds)
How do you calculate the activity of a sample
-As a sample decays, its activity goes down:
A=A0e^-lamdat (t is time in seconds)
What are the different uses for different half lives?
-Radioactive substances are extremely useful. You can sue them for all sorts - to date organic material, diagnose medical problems, sterilise foods and in smoke alarms. Knowledge about half lives can be used for:
1. Radioactive dating of objects
2. Medical diagnosis
How are half-lives used in radioactive dating of object tis?
1. The radioactive isotope carbon-14 is used in radioactive dating
2. Living plants take in carbon dioxide form the atmosphere as part of photosynthesis, including the radioactive isotope carbon-14
3. When they die the activity of carbon-14 in the plant starts to fall, with a half life of around 5730 years
4. Archaeological finds made from once living material (like wood) can be tested to find the current amount of carbon-14 in them, and date them
How are half-lives used in medical diagnosis?
1. Radioactive tracers are used to help diagnose patients
2. Technetium-99m is suitable for this size because it emits gamma radiation, has a half-life of 6 hours (long enough for data to be recorded, but short enough to limit the radiation to an acceptable level) an decays to a much more stable isotope
Why are long half-lives dangerous?
1. As well as being useful radioactive substances can be dangerous too
2. This is an even bigger problem if the substances stay radioactive for a long time
3. Some isotopes found in waste products of nuclear power generation have incredibly long half-lives
4. This means that we must plan ahead about how nuclear waste will be stored, e.g. in water tanks or sealed underground, to precent dame to the environment or people not only now but into the future too
Why are dome nuclei more stable than others?
-The nucleus is under the influence of the strong nuclear force holding it together and the electromagnetic force pushing the protons apart
-It is a very delicate balance and it is easy for a nucleus to become unstable. You can get stability graph by plotting Z (atomic number) against N (number of neutrons)
When will a nucleus become unstable?
-A nucleus will be unstable if it has:
1. Too many neutrons
2. Too few neutrons
3. Too many nucleons altogether i.e. it's too heavy
4. Too much energy
Describe alpha emission
-Alpha emission happens in heavy nuclei
1. When an alpha particle is emitted, the proton number decrease bu two, and the nucleon number decreases by four
2. Alpha emission only happens in very heavy atoms, like uranium and radium
3. The nuclei of these two atoms are too massive to be stable
Describe beta minus emission
-Beta minus emission happens in neutron rich nuclei
1. Beta-minus (usually just called beta) decay is the mission of one electron form the nucleus along with an antineutrino
2. Beta decay happens in isotopes that are "neutron rick" (i.e.i they have many more neutron than protons in their nucleus)
3. when a nucleus ejects a beta particle, one of the neutrons in the nucleus is change into a proton
4. when a beta minus particle is emitted: the proton number increases by one and the nucleon number stays the same
What happens in beta plus emission?
-In beta-plus emission a proton gets changed into a neutron
-The proton number decreases by one, and the nucleon number stays the same
When is gamma radiation emitted?
-Gamma radiation is emitted form nuclei with too much energy
1. After alpha or beta decay, the nucleus often has excess energy - it is excites. This energy is lost by emitting a game ray
2. During gamma emission, there is no change to the nuclear constituents - the nucleus just loses excess energy
3. Another way that gamma radiation is produced is when a nucleus captures one of its own orbiting electrons
4. Electron capture causes a proton to change into a neutron and this means the nucleus unstable and it emits gamma radiation
-The artificial isotope technetium-99m is formed in an excited state form the decay of another elements and it is used as a tracer in medical imaging
What are the conservation rules in nuclear reactions?
In every nuclear reaction energy, momentum, charge and nucleon number must be conserved
What is the mass defect equivalent to?
-The mass defect is equivalent to the binding energy
1. The mass of a nucleus is less than the mass of its constituent parts - the difference is called the mass defect
2. Einstein's equation E=mc^2, syas tuta mass and energy are equivalent and it applies to all energy changes
3. So, as nucleons join together the total mass decreases - this 'lost' mass is converted into energy and released
4. The amount of energy related is equivalent to the mass defect
5. If you pulled the nucleus completely apart, the energy you'd have to use to do it wold be the same as the energy released when the nucleus formed
-The energy needed to separate all of the nucleons is called the binding energy (measure in Mev) and it is equivalent to the mass defect
6. A mass defect of 1 u is equivalent to about 931.5 Mev of being energy
What is the average binding energy per nucleon at a maximum?
-The average binding energy per nucleon is at a maximum around N=50
-A useful way of comparing boning energies of different nuclei is to look at the average binding energy per nucleon
1. A graph of average binding energy per nucleon against nucleon number, for all elements shows a curve, high average biding energy per nucleons means that more energy is needed to remove nucleons from the nucleus
2. In other words, the most stable nuclei occur around the maximum point on the graph, which is at a nucleon number 56 (i.e. Iron Fe)
3. Combining small nuclei is called nuclear fusion and this increases the average binding energy per nucleon dramatically, which means a lot of energy is related during nuclear fission
4. Fission is when large nuclei are split in two, the nucleon numbers of the two new nuclei are smaller than the original nucleus, which means there is an increase in the average binding energy per nucleon. So, energy is related during nuclear fission ( but not as much energy per nucleon as in nuclear fusion)