6.3.1 Beta-minus and beta-plus decay

Beta decay in unstable nuclei

1. A nucleus is held together by the balance between the strong nuclear force pulling all the nucleons together and the electrostatic repulsion pushing the protons apart.
2. When a nucleus holds too many neutrons or too many protons for that balance to hold, it is unstable and it will eventually decay.
3. Beta decay is the route an unstable nucleus takes when its problem is the ratio of neutrons to protons rather than its total size, so no nucleons are thrown out of the nucleus at all.
4. Instead, one nucleon changes identity inside the nucleus, and a small light particle is created and thrown out to carry away the charge.
5. There are two versions of this, and which one happens depends on which nucleon the nucleus has too many of.
   1. A nucleus with too many neutrons turns a neutron into a proton and emits an electron, which is called beta-minus decay and written ${\beta }^{-}$ decay.
   2. A nucleus with too many protons turns a proton into a neutron and emits a positron, which is called beta-plus decay and written ${\beta }^{+}$ decay.
6. The two emitted particles are antiparticles of each other, so they have the same very small relative mass but opposite relative charge.

Beta-minus decay

1. Inside a neutron-rich nucleus, a single neutron changes into a proton and an electron, and the electron is immediately expelled from the nucleus.
2. In words, the change to the nucleon is $neutron\to proton+electron$.
3. Using particle symbols, the same change is $n\to p+e^{-}$.
4. Written with mass numbers and charges, so that both quantities can be seen to balance, the change is ${}_0^{1}n{\to }_1^{1}p{+}_{-1}^{0}e$.
5. The emitted electron is the beta-minus particle, and in a nuclear equation it is written as ${}_{-1}^{0}e$ or ${}_{-1}^0\beta$.
6. Both symbols carry the same information: a mass number of $0$, because an electron contains no protons or neutrons, and a charge of $-1$, because it carries one electron charge.
7. The electron that leaves is created in the nucleus at the moment of decay, and it is not one of the electrons that was orbiting the atom beforehand.
8. Beta-minus emitters are common among the heavy nuclei produced in reactors and among the daughter products of long decay chains, because those nuclei are typically left neutron-rich.

Beta-plus decay

1. Inside a proton-rich nucleus, a single proton changes into a neutron and a positron, and the positron is immediately expelled from the nucleus.
2. In words, the change to the nucleon is $proton\to neutron+positron$.
3. Using particle symbols, the same change is $p\to n+e^{+}$.
4. Written with mass numbers and charges, the change is ${}_1^{1}p{\to }_0^{1}n{+}_{+1}^{0}e$.
5. The emitted positron is written ${}_{+1}^{0}e$ or ${}_{+1}^0\beta$, with a mass number of $0$ and a charge of $+1$.
6. A positron is a form of antimatter, so once it has left the nucleus it travels only a very short distance through matter before it meets an ordinary electron and the pair is annihilated.
7. Because a positron is destroyed so quickly, beta-plus emitters are much harder to keep and store than beta-minus emitters, and they are usually made artificially.

Comparing the two beta decays

1. Both decays start with an unstable nucleus, change one nucleon into the other kind of nucleon, and emit one light particle from the nucleus.
2. The differences all follow from which nucleon changes.
   1. In ${\beta }^{-}$ decay a neutron is the nucleon that changes, so the neutron count falls by one and the proton count rises by one.
   2. In ${\beta }^{+}$ decay a proton is the nucleon that changes, so the proton count falls by one and the neutron count rises by one.
3. The emitted particles differ only in the sign of their charge, which is what the minus and plus in the two names record.
4. Neither decay ejects a nucleon from the nucleus, which is what separates beta decay from alpha decay and from neutron emission.
5. Neither decay can be triggered or prevented, because which nucleus decays and when is settled by chance alone.

6.3.2 Effects of decay on the nucleus

The two numbers that describe a nucleus

1. A nucleus is written in the form ${}_Z^{A}X$, where $X$ is the chemical symbol, $A$ is the mass number and $Z$ is the atomic number.
2. The atomic number is the count of protons, and it alone decides which element the nucleus belongs to, so any decay that changes $Z$ changes the element.
3. The mass number is the count of protons plus neutrons, so the neutron count of a nucleus is always $A-Z$.
4. Every radioactive decay removes something from the nucleus or converts one nucleon into another, so every decay leaves $A$ and $Z$ changed in a way fixed by what was emitted.
5. The nucleus that is left behind after a decay is the daughter nucleus, and the nucleus that decayed is called the parent nucleus.
6. Because both numbers are conserved across a decay, working out the daughter is a matter of subtracting the mass number and the charge of the emitted particle from the parent.

Alpha decay

1. An alpha particle is a tightly bound group of two protons and two neutrons, identical to a helium nucleus, and it is written ${}_2^4\alpha$ or ${}_2^{4}He$.
2. Alpha decay happens in very heavy nuclei, where the electrostatic repulsion between a large number of protons makes the whole nucleus too large to hold together.
3. Ejecting an alpha particle removes four nucleons at once, which is the fastest way for such a nucleus to shed both size and positive charge.
4. The alpha particle carries away a mass number of $4$, so the mass number of the nucleus falls by $4$.
5. It also carries away a charge of $+2$, so the atomic number falls by $2$.
6. Since the atomic number has changed, the daughter nucleus is a different element, two places back in the periodic table.
7. In general form, alpha decay is ${}_Z^{A}X{\to }_{Z-2}^{A-4}Y{+}_2^4\alpha$.

Beta-minus and beta-plus decay

1. In beta-minus decay a neutron becomes a proton and an electron is emitted, and the electron is written ${}_{-1}^{0}e$.
2. Because the electron has a mass number of $0$, the total nucleon count is unchanged, so the mass number stays the same.
3. Because a neutron has been replaced by a proton, the atomic number rises by $1$, and the daughter is the next element up.
4. In general form, beta-minus decay is ${}_Z^{A}X{\to }_{Z+1}^{A}Y{+}_{-1}^{0}e$, as in ${}_6^{14}C{\to }_7^{14}N{+}_{-1}^{0}e$.
5. In beta-plus decay a proton becomes a neutron and a positron is emitted, and the positron is written ${}_{+1}^{0}e$.
6. The mass number again stays the same, for the same reason, but the atomic number falls by $1$, so the daughter is the previous element.
7. In general form, beta-plus decay is ${}_Z^{A}X{\to }_{Z-1}^{A}Y{+}_{+1}^{0}e$, as in ${}_{11}^{22}Na{\to }_{10}^{22}Ne{+}_{+1}^{0}e$.
8. Both beta decays therefore change the element without changing the mass of the nucleus in any measurable way, because the neutron count and proton count trade places.

Gamma emission and nuclear rearrangement

1. Gamma radiation is not a particle at all; it is a very high frequency electromagnetic wave carrying energy away from the nucleus.
2. A gamma ray has no mass number and no charge, so it is written ${}_0^0\gamma$.
3. The direct consequence is that after gamma emission the mass number stays the same, the atomic number stays the same, and the element does not change.
4. What does change is the energy of the nucleus, which is left lower than it was before.
5. Gamma emission normally follows another decay rather than happening on its own, because an alpha or beta decay usually leaves the daughter nucleus with its nucleons in a high energy arrangement.
6. That high energy state is described as an excited nucleus, and it settles by nuclear rearrangement: the protons and neutrons shift into a lower energy arrangement and the surplus energy leaves as a gamma ray.
7. Because gamma emission needs no nucleon to leave and no nucleon to change, it is the only one of these processes that leaves the identity of the nucleus completely untouched.
8. In general form, gamma emission is ${}_Z^A{X}^{\ast }{\to }_Z^{A}X{+}_0^0\gamma$, where the asterisk marks the excited nucleus.

Neutron emission

1. A neutron released from a nucleus is written ${}_0^{1}n$, giving it a mass number of $1$ and a charge of $0$.
2. The nucleus therefore loses one nucleon, so its mass number falls by $1$.
3. The neutron carries no charge, so the proton count is untouched and the atomic number stays the same.
4. Since the atomic number is unchanged, the daughter is the same element as the parent, but a different isotope of it, with one fewer neutron.
5. In general form, neutron emission is ${}_Z^{A}X{\to }_Z^{A-1}X{+}_0^{1}n$, so oxygen-17 emitting a neutron gives ${}_8^{17}O{\to }_8^{16}O{+}_0^{1}n$.
6. Neutron emission is the one decay in this set that changes the isotope without changing the element, which makes it easy to tell apart from a beta decay in an equation.

6.3.3 Balancing nuclear equations

What a nuclear equation records

1. Every nucleus and particle in a nuclear equation is written as ${}_Z^{A}X$, with the mass number $A$ on top and the charge number $Z$ below.
2. For a nucleus the charge number is simply the proton number, because each proton carries one unit of positive charge and the neutrons carry none.
3. For an emitted particle the charge number is that particle's own charge, so a beta particle takes $Z=-1$ and a gamma ray takes $Z=0$.
4. Two quantities are conserved across the arrow, which is what makes the equation solvable.
   1. The total mass number on the left equals the total mass number on the right, because nucleons are neither created nor destroyed.
   2. The total charge on the left equals the total charge on the right, because charge cannot be created or destroyed.
5. Balancing a nuclear equation therefore means finding the missing numbers that make both of those totals agree.
6. The two totals are kept completely separate: the top numbers are added only to other top numbers, and the bottom numbers only to other bottom numbers.
7. This is not the same task as balancing a chemical equation, where whole atoms are counted and no atom ever changes into another element.

The symbols you need

1. An alpha particle is ${}_2^4\alpha$, sometimes written ${}_2^{4}He$, because it is two protons and two neutrons.
2. A beta-minus particle is ${}_{-1}^{0}e$, sometimes written ${}_{-1}^0\beta$, because it is an electron with no nucleons and one unit of negative charge.
3. A positron is ${}_{+1}^{0}e$, sometimes written ${}_{+1}^0\beta$, because it has no nucleons and one unit of positive charge.
4. A gamma ray is ${}_0^0\gamma$, because it carries energy but neither nucleons nor charge.
5. A neutron is ${}_0^{1}n$, because it is one nucleon with no charge.
6. A proton is ${}_1^{1}p$, because it is one nucleon carrying one unit of positive charge.
7. Once these six symbols are known, every balancing task reduces to two subtractions.

The method for balancing

1. Write the equation out with the unknown labelled, using $A$ for the missing top number and $Z$ for the missing bottom number.
2. Add the top numbers on the left, then add the top numbers on the right.
3. Set those two totals equal to each other and solve for the missing mass number.
4. Add the bottom numbers on the left, then add the bottom numbers on the right, remembering that a negative charge number reduces the total.
5. Set those two totals equal to each other and solve for the missing charge number.
6. Use the data supplied with the question, such as a section of the periodic table, to turn the charge number into an element symbol if a symbol is wanted.
7. Substitute both answers back in and check that each total still agrees, since this catches a sign slip in seconds.

6.4.1 Activity and its decrease over time

Activity and its unit

1. A radioactive sample contains an enormous number of unstable nuclei, and each one will decay at some point, but they do not all decay together.
2. Activity counts how fast the sample as a whole is decaying, measured as the number of nuclei that break down each second.
3. The unit of activity is the becquerel, symbol $Bq$, and $1Bq$ means exactly one decay per second.
4. Because one decay per second is a tiny rate, real sources are quoted in kilobecquerels or megabecquerels, where $1kBq=1000Bq$ and $1MBq=1000000Bq$.
5. Activity depends on two things: how many undecayed nuclei are still present, and how likely each of those nuclei is to decay in the next second.
6. The second of those is fixed for a given isotope and cannot be altered, so heating a source, dissolving it or grinding it up has no effect on its activity.
7. The first can only fall, because every decay permanently removes one undecayed nucleus from the sample.
8. Activity is a rate, not an amount, so a source with a high activity is not necessarily one that contains a lot of material; it may simply be decaying quickly.

Why activity falls over time

1. At the start there is a large stock of undecayed nuclei, so a large number of them happen to decay each second and the activity is high.
2. Every one of those decays converts an unstable nucleus into a different nucleus, so the stock of undecayed nuclei is smaller a second later.
3. With fewer nuclei available to decay, fewer of them decay in the next second, so the activity is lower.
4. That lower activity in turn removes nuclei more slowly, so the fall in activity itself becomes gentler as time goes on.
5. The result is a curve that starts steep and flattens out, always heading towards zero but never quite reaching it, which is described as exponential decay.
6. A useful way to state the mechanism is that the activity at any moment is proportional to the number of undecayed nuclei remaining, so as one falls the other falls with it.
7. The fall is not perfectly smooth from one reading to the next, so a run of measurements has to be repeated and averaged before the trend can be trusted.

Measuring activity in the laboratory

1. A Geiger-Muller tube connected to a counter is the instrument used to follow how a source is decaying.
2. What the counter records is a count rate, in counts per second, and this is not the same as the activity of the source.
3. The count rate is always lower than the activity, for three reasons.
   1. Radiation is emitted in all directions, so only the fraction aimed at the tube can be detected.
   2. Some radiation is absorbed by the air and by the window of the tube before it can be registered.
   3. The tube does not respond to every particle that enters it, and it detects alpha radiation very poorly compared with beta and gamma.
4. The count rate is still a valid measure of how the activity is changing, because the fraction detected stays roughly constant if the detector and the source are not moved.
5. Every reading also includes background radiation, which is present in the room whether or not the source is there.
6. Background must therefore be measured with the source removed and subtracted from every reading, giving a corrected count rate.
7. In symbols, $corrected\; count\; rate=measured\; count\; rate-background\; count\; rate$.

6.4.2 Half-life and its random nature

What half-life means

1. Activity falls away smoothly towards zero, so there is no moment at which a source can be said to have finished decaying, and no way to quote a simple lifetime for it.
2. Half-life solves this by timing the loss of a fixed fraction rather than a fixed amount, and the fraction chosen is one half.
3. There are two equivalent statements of it, and either is acceptable.
   1. The time taken for half the undecayed nuclei in a sample to decay.
   2. The time taken for the activity of a source to fall to half its starting value.
4. The two agree because activity is proportional to the number of undecayed nuclei, so halving one halves the other.
5. Half-life is a time, so it is quoted in seconds, hours, days or years, and never as a fraction or a rate.
6. Half-life is a property of the isotope, so every sample of the same isotope shares it, and it cannot be altered by heating, cooling, dissolving, compressing or chemically reacting the material.
7. A short half-life means the activity dies away quickly, and a long half-life means a lower activity that persists for a very long time.

Half-life is constant along the curve

1. The defining property is that the same interval of time removes the same fraction of what is left, wherever on the curve you begin.
2. So the time to fall from the full amount to a half is the same as the time to fall from a half to a quarter, and the same again from a quarter to an eighth.
3. This is why the fall is described as exponential: the step down is always proportional to the amount currently present.
4. It also explains the shape of the graph, which is steep at the start where there is most left to lose and shallow later where there is least.
5. Because the fraction lost is fixed, the amount remaining never reaches zero on the graph, and the curve approaches the time axis without meeting it.
6. A practical consequence is that half-life can be measured from any convenient pair of points on a curve, not only from the starting value, and several such measurements should agree.

Why decay is random

1. Nothing inside a nucleus counts down to its decay, and a nucleus does not age, wear out or become more likely to decay the longer it has already survived.
2. Every undecayed nucleus of a given isotope simply carries the same fixed chance of decaying in the next second.
3. It is therefore impossible to predict when a particular nucleus will decay, and impossible to say which nucleus in a sample will be next.
4. It is equally impossible to make a chosen nucleus decay sooner or later, because nothing done to the material changes that fixed chance.
5. What can be predicted is the behaviour of a very large number of nuclei taken together, and this is exactly what half-life does.
6. Even a very small sample holds nuclei in numbers of the order of $10^{20}$, so although each one is unpredictable, the fraction that decays in a given interval is almost exactly the same every time.
7. Half-life is therefore a statistical quantity: it predicts the activity of a large sample reliably while saying nothing whatever about any individual nucleus.
8. The randomness is still visible when the numbers involved are small, which is why a count taken over a few seconds jumps about while the same source counted over several minutes gives a steady value.
9. Readings taken late in the decay scatter far more than early ones, because by then too few nuclei remain for the averaging to work well.
10. The two ideas fit together rather than contradicting each other: the process is random at the level of one nucleus and predictable at the level of a whole sample.

6.4.3 Half-life calculations

Counting half-lives

1. Every half-life calculation turns on one number: how many half-lives have passed.
2. The number of half-lives is $n=\frac{t}{t_{1/2}}$, where $t$ is the total elapsed time and $t_{1/2}$ is the half-life.
3. Both times must be in the same unit before dividing, so a time given in hours and a half-life given in minutes must be converted first.
4. Each half-life multiplies whatever is left by $\frac{1}{2}$, so after $n$ half-lives the fraction remaining is ${\left(\frac{1}{2}\right)}^n=\frac{1}{2^n}$.
5. It is worth knowing the first few values by sight: $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{8}$, $\frac{1}{16}$, $\frac{1}{32}$, $\frac{1}{64}$ for $n=1$ to $6$.
6. The same fraction applies whether the quantity being tracked is the activity, the count rate or the number of undecayed nuclei, because all three fall together in proportion.
7. For activity, this gives $A=A_0\times {\left(\frac{1}{2}\right)}^n$, where $A_0$ is the starting activity and $A$ is the activity after $n$ half-lives.
8. For nuclei, the same relationship is $N=N_0\times {\left(\frac{1}{2}\right)}^n$.
9. The fraction that has decayed is whatever is left over, so it is $1-\frac{1}{2^n}$; after $3$ half-lives, $\frac{1}{8}$ remains and $\frac{7}{8}$ has decayed.
10. Reading the question carefully matters here, because it may ask for the amount remaining, the amount decayed, or the ratio between them, and these are three different answers.

The four question types

1. Type one: find the amount left after a given time. Work out $n$, then halve the starting value $n$ times, or multiply it by $\frac{1}{2^n}$.
2. Type two: find the time for a given fall. Count how many halvings take the starting value to the final value, then multiply that count by the half-life, since $t=n\times t_{1/2}$.
3. Type three: find the half-life. Count the halvings between the two given values to get $n$, then divide the elapsed time by it, since $t_{1/2}=\frac{t}{n}$.
4. Type four: express the fall as a ratio. Give the answer in the form final to initial, such as $1:8$, or as the fraction $\frac{1}{8}$, whichever the question asks for.
5. When $n$ is not a whole number, halving repeatedly will not reach the answer exactly, and the value must be read from a graph instead.
6. Working in whole halvings is the quickest and safest route whenever the numbers allow it, because it needs no power key on the calculator.

Reading a decay curve

1. A decay curve plots activity, count rate or number of undecayed nuclei on the vertical axis against time on the horizontal axis.
2. Start by reading the value on the vertical axis at $t=0$, which is the starting value $A_0$.
3. Halve that value, find the halved value on the vertical axis, and draw a horizontal construction line across to the curve.
4. From that meeting point, drop a vertical construction line down to the time axis and read off the time, which is the half-life.
5. Repeat the same steps starting from a different point on the curve, for instance from the half value down to the quarter value, and check that the two times agree.
6. Averaging two or three such readings gives a better value than one, because the curve is drawn through scattered points.
7. Leave the construction lines on the graph, since they show the method and are what a marker looks for.
8. Where the vertical axis is a count rate, subtract any background count rate the question supplies before halving, otherwise the halving is applied to the wrong starting value.
9. To read the value at a time between plotted points, go up from the time axis to the curve and across, rather than trying to calculate it.

6.6.1 Diagnosis and treatment using radiation

Treating tumours with radiation

1. The radiation used is high-energy gamma rays or high-energy X-rays, because only very penetrating radiation can reach a tumour buried inside the body.
2. As the radiation passes through a cell it ionises molecules, and the damage that matters most is the damage done to the cell's DNA.
3. A cell with badly damaged DNA cannot copy it correctly, so the cell fails when it next tries to divide and it dies.
4. Tumour cells divide far more often than most healthy cells and are worse at repairing DNA damage, so the same dose kills a much greater share of them.
5. Healthy cells in the path of the radiation are damaged too, which is what causes the side effects of treatment, so every method of delivering the radiation is designed to give the largest possible dose to the tumour and the smallest possible dose everywhere else.
6. The total dose is usually split into many small fractions given on different days, which gives healthy tissue time to repair between sessions while the tumour is worn down.
7. The radiation can be delivered from a machine outside the body or from a source placed inside it.

External radiotherapy

1. A machine outside the patient produces a narrow beam of high-energy radiation and directs it at the tumour, so no radioactive material ever enters the body.
2. The beam is shaped by a collimator so that its cross-section matches the outline of the tumour as closely as possible.
3. The machine is then rotated around the patient, so the beam enters the body from many different directions during the session.
4. Every beam direction passes through the tumour, so the tumour receives the sum of all the doses and ends up with a very large total.
5. Any one region of healthy tissue lies in the path of only one or two of those directions, so it receives a much smaller total than the tumour does.
6. Advantages: nothing is implanted, so no surgery is needed; the patient is not radioactive at any point and can go home straight away; deep tumours can be reached; and the direction, shape and size of the dose can be adjusted between sessions.
7. Disadvantages: the radiation has to travel through healthy tissue on its way in and out, side effects such as tiredness, reddened skin and hair loss in the treated area are common, many sessions are needed over several weeks, and the patient must be positioned very accurately each time.

Internal radiotherapy

1. A radioactive source is placed inside the body, either in the tumour itself or immediately next to it.
2. The source may be a small sealed pellet or rod inserted during a short procedure, or a radioactive substance that the body itself concentrates in the target tissue.
3. An overactive thyroid or a thyroid tumour, for example, can be treated with radioactive iodine, because the thyroid gland absorbs iodine from the blood whether or not the nuclei are stable.
4. The radiation spreads out from the source in all directions, so its intensity falls rapidly with distance.
5. Tissue touching the source therefore receives an extremely large dose while tissue a few centimetres further away receives very little, which is exactly the pattern the treatment wants.
6. Advantages: the tumour gets a very high dose, healthy tissue further away is largely spared, treatment continues steadily while the source stays in place, and fewer hospital visits are needed.
7. Disadvantages: placing the source usually needs an invasive procedure, staff have to handle a radioactive source, the patient is radioactive while the source is inside them and so must limit close contact with visitors, and the method only suits tumours that can be reached or that take up a particular substance.

Tracers in diagnosis

1. A tracer is swallowed, injected or inhaled, depending on which organ is being investigated, and is carried around the body by the blood.
2. The radioactive atoms are attached to a chemical the target tissue takes up naturally, so the tracer collects where the doctor wants to look.
3. A gamma camera outside the patient detects the radiation coming out and builds a picture of where the tracer has gone.
4. A medical tracer must be a gamma emitter, because gamma radiation is the only kind penetrating enough to escape the body and reach the camera; alpha and beta radiation would be absorbed by the surrounding tissue and would only add to the patient's dose.
5. It must also have a short half-life, long enough for the scan to be completed but short enough that the activity inside the patient falls away within hours rather than years.
6. Technetium-99m is the isotope used most often, because it emits gamma radiation only and has a half-life of about $6hours$.
7. The doctor is looking for tissue that takes up more or less tracer than expected, since that pattern shows how the organ is working rather than just what shape it is.
8. Tracers are used to follow blood flow, to check how well a kidney or a thyroid gland is functioning, to find blockages in the circulation or the digestive system, and to locate secondary tumours in bone.

How a PET scanner works

1. The patient is injected with a tracer whose nuclei emit positrons rather than gamma rays, most often fluorine-18 attached to a molecule that behaves like glucose.
2. Tissue that is working hardest uses the most glucose, so the most active tissue, including many tumours, takes up the most tracer.
3. Each emitted positron travels only a very short distance through tissue before it meets an electron, of which there are enormous numbers in every atom around it.
4. A positron and an electron are a particle and its antiparticle, so when they meet they annihilate: both are destroyed and their mass is converted into energy.
5. That energy leaves as two gamma rays travelling in opposite directions, which is required because the pair had almost no momentum before they met.
6. A ring of detectors surrounds the patient, and the electronics look for two gamma rays arriving on opposite sides of the ring at almost the same instant.
7. Each such pair of detections means an annihilation happened somewhere along the straight line joining the two detectors.
8. A computer collects millions of these lines and finds the regions where they cross most often, and those regions are where the tracer is concentrated.
9. The result is a three-dimensional image showing how active each part of the body is, which is information that an X-ray image of structure alone cannot give.
10. PET scans are used to find tumours, to check whether a tumour is still active after treatment, and to study how the brain and the heart are working.

Making PET isotopes nearby

1. The isotopes that emit positrons have very short half-lives: about $110minutes$ for fluorine-18 and only about $20minutes$ for carbon-11.
2. A short half-life is chosen deliberately, because it means the activity inside the patient falls away within a few hours and the dose is kept small.
3. The same property applies before the scan as well, so the activity is falling steeply from the moment the isotope is made.
4. A long journey would use up several half-lives, and once too few nuclei are left the number of annihilations per second is too small to build a clear image.
5. Giving the patient a much larger amount to compensate is not an option, because that would raise the dose and undo the reason for using a short-lived isotope.
6. The isotopes are therefore made in a cyclotron on the hospital site or at a centre close to it, attached to the tracer molecule immediately, and injected within a few hours.
7. This is why PET scanning is expensive and why it is available at far fewer hospitals than ordinary X-ray imaging.