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The two nuclear changes that have to be made to happen, where their energy comes from, and what ionizing radiation does when it reaches something living.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to tell fission from fusion by which side the heavy nucleus is on rather than by the energy, audit either equation for conservation of mass number and atomic number with the free neutrons counted, and say how a chain reaction multiplies from one generation to the next. You will be able to explain where the energy comes from as an accounting identity between mass and energy, say why an alpha emitter is nearly harmless outside the body and the worst of the three inside it, and name the three defenses against a source and spot a described procedure that gives one up.
You can predict a decay mode from two numbers, write the equation for it, and work out how long a sample takes to halve. All of that was about a nucleus changing on its own. This lesson is about the two nuclear changes that have to be made to happen, about where the energy of any of it comes from, and about what that energy does when it arrives somewhere living.
| Term | What it means |
|---|---|
| Fission | A heavy nucleus coming apart into two middling ones, usually struck by a neutron. |
| Fusion | Two light nuclei joining into a heavier one. |
| Chain reaction | Fission that keeps itself going because each split's neutrons cause the next. |
| Ionizing radiation | Radiation energetic enough to knock electrons off atoms it passes. |
| Sealed source | A radioactive sample inside a container it cannot escape. |
Add up the masses of everything that goes into a nuclear change, and add up the masses of everything that comes out. The two totals are not the same. What comes out weighs very slightly less, and that missing mass is the energy released.
That is the accounting identity, and the reason the numbers are so startling is the conversion factor. Energy equals the missing mass multiplied by the speed of light squared, and the speed of light squared is about $9 \times 10^{16}$ in meters and seconds. So a mass difference far too small to weigh gives an energy far too large to ignore: splitting a single gram of uranium releases roughly as much energy as burning three tons of coal.
This course states that relationship and does not ask you to compute with it.
Which way do the sizes have to move? There is a most-stable size, and it is around iron. Nuclei heavier than iron release energy by getting smaller; nuclei lighter than iron release energy by getting larger. That is the whole reason there are two processes rather than one:
And through all of it both counts still balance exactly: the missing mass is a few parts in a thousand and never shows in a whole-number count.
Another way: picture
Picture a valley with iron at the bottom. Very heavy nuclei sit high up one side and roll downhill by breaking into pieces; very light nuclei sit high up the other side and roll downhill by sticking together. Either way something rolls down, and what it releases on the way is the energy. Nothing rolls uphill on its own, which is why nobody gets energy out of splitting iron.
Another way: steps
To tell which process an equation shows:
Write every particle with both numbers. Including each free neutron, $^{1}_{0}\mathrm{n}$, and any coefficient in front of it — three neutrons are three times 1 and 0.
Total each side. Mass numbers left, mass numbers right, atomic numbers left, atomic numbers right.
Confirm the pairs agree. Mass number left equals right; atomic number left equals right.
Name the process from where the largest nucleus sits: on the left, fission; on the right, fusion.
For a chain reaction, multiply: each generation's neutrons times the neutrons per split gives the next generation.
For a hazard question, name the kind of radiation and the defense that applies: time, distance, shielding, or keeping the source sealed.
Check the work. A fission audit that fails by two or three in the mass number almost always means free neutrons were left out. A fusion product heavier than iron, or a fission product heavier than the parent, is impossible and means the sides were read backwards. And a dose that rises as someone moves away has the distance rule inverted.
Totaling mass numbers and atomic numbers is allowed for the same reason as in the last lesson: protons and neutrons are conserved in number, and charge is conserved exactly.
Ignoring the missing mass in the totals is allowed because it is tiny compared with a whole nucleon — a fraction of one percent of the total — so it never moves a whole-number count, even though it accounts for all the energy.
Naming the process by size is allowed because energy is released either way; only the direction toward iron distinguishes the two.
Multiplying for a chain reaction is allowed because each neutron acts independently, so the count of the next generation is the count of this one times the yield per split.
Using the square of the distance for dose is allowed because a source sends radiation out in all directions, spread over the surface of a sphere whose area grows with the square of its radius. Twice as far, the same radiation covers four times the area.
All three kinds of radiation carry enough energy to knock electrons off atoms they pass. In a living cell that means breaking molecules — including the molecule that carries the instructions for making more cells. A cell with a broken strand usually mends it, sometimes dies, and occasionally mends it wrongly and goes on dividing, which is the mechanism behind the raised cancer risk that follows a large dose.
That is why the hazard is not the same as the penetrating power. Gamma is the hardest to stop, so an external gamma source is the dangerous one; alpha is stopped by skin, so an external alpha source is almost harmless — and an alpha emitter swallowed or breathed in is the worst of the three by a distance, because now all that ionizing happens inside, among cells, with nothing in between. Radon in a basement is dangerous for exactly this reason.
There are three defenses and they are the whole subject:
And a fourth for anything that is not sealed: containment, keeping it in a box and out of the air, because the defenses above assume the source stays outside you.
This course teaches hazard recognition and no procedure. Nothing in it asks anyone to handle a source, and the practice items describe a procedure and ask what is wrong with it.
A reactor is a chain reaction held at exactly one. Each split releases two or three neutrons; control rods made of boron or cadmium absorb neutrons; the rods go further in until, on average, exactly one neutron from each split goes on to cause the next. One means steady. Below one the reaction dies out. Above one it grows, which is what the rods exist to prevent.
A moderator — water or graphite — slows the neutrons down, because uranium-235 is far more likely to be split by a slow neutron than a fast one. A coolant carries the heat away to boil water and drive a turbine, which is the only ordinary part of the whole machine.
What is left in the fuel afterwards is the difficulty. The fission fragments are middling nuclei with far too many neutrons for their size — cesium-137 and strontium-90 — so they are beta emitters, and intensely active precisely because their half-lives are short. Some of the uranium-238 has meanwhile absorbed neutrons and become plutonium-239, which the last lesson gave a half-life of about 24 000 years. So spent fuel is fiercely radioactive for decades and a problem for far longer, and nothing chemistry can do reaches either of those, because a half-life is a property of the nucleus.
About a fifth of the electricity used in the United States comes from roughly 90 nuclear reactors, from Plant Vogtle in Georgia to the Palo Verde station in the Arizona desert, and every one of them is a fission chain reaction held at exactly one. The fuel is uranium enriched to about 4 or 5 percent uranium-235, pressed into ceramic pellets the size of a fingertip.
The energy is the missing-mass accounting at work. One pellet, about 7 grams, produces roughly as much electricity as a ton of coal, because the products of each split weigh slightly less than the uranium and neutron that went in. Across a year, a 1,000-megawatt reactor turns only about a kilogram of mass into energy — yet that is enough to power several hundred thousand homes.
The chain is controlled by neutron arithmetic. Each split releases two or three neutrons; control rods absorb the surplus so that exactly one, on average, causes the next split. Water in the core slows the neutrons, making them more likely to split uranium-235, and carries the heat to steam generators.
The spent fuel is the hard part. It holds cesium-137 and strontium-90, with half-lives of about 30 years, and plutonium with half-lives of thousands. American plants store it first in pools and then in steel-and-concrete casks on site, and where to keep it for the very long term is still being decided — a question set entirely by half-life arithmetic that no chemistry can change.
Every second the Sun fuses about 600 million tons of hydrogen into helium, and about 4 million tons of mass disappear as energy. That missing mass is the sunlight reaching Earth eight minutes later.
The free neutrons are left out of the balance. A fission equation looks unbalanced until the two or three neutrons on the right are counted, and each of them is a mass number of 1 and an atomic number of 0. Leaving them out is the commonest reason an audit fails.
Fission and fusion are told apart by the energy. They cannot be: energy comes out of both. What tells them apart is the direction the sizes moved.
Mass is thought to be destroyed. It is accounted for as energy, and the total of the two together is exactly conserved.
Penetrating power is confused with danger. Alpha is the least penetrating and the most ionizing, so it is the least dangerous of the three outside the body and the worst of them inside it.
A reactor is thought to be able to explode like a bomb. A bomb needs uranium enriched far past reactor fuel and assembled in a particular way. A reactor accident is a fire, a steam explosion or a meltdown, and the hazard is the fission products getting out — which is serious, and is a different thing.
Irradiated things are thought to become radioactive. Food passed through a gamma beam to kill bacteria, or an instrument sterilized the same way, is not radioactive afterwards: gamma rays passing through leave no nuclide behind. Contamination — actual radioactive material landing on something — is the case where it does, and the two are worth keeping apart.
Write the equation.
$\mathrm{^{235}_{92}U} + \mathrm{^{1}_{0}n} \rightarrow \mathrm{^{141}_{56}Ba} + \mathrm{^{92}_{36}Kr} + 3\,\mathrm{^{1}_{0}n}$
Every particle with both numbers.
Total the left mass numbers.
$235 + 1 = 236$
Count the incoming neutron.
Total the right mass numbers.
$141 + 92 + 3 \times 1 = 236$
Three neutrons out.
Total the atomic numbers.
$92 + 0 = 92; \ 56 + 36 + 0 = 92$
Neutrons carry no charge.
Name the process.
$\text{big nucleus on the left: fission}$
Three neutrons out make a chain possible.
Write the equation.
$\mathrm{^{2}_{1}H} + \mathrm{^{3}_{1}H} \rightarrow \mathrm{^{4}_{2}He} + \mathrm{^{1}_{0}n}$
Deuterium and tritium.
Total the left mass numbers.
$2 + 3 = 5$
Two light nuclei.
Total the right mass numbers.
$4 + 1 = 5$
Helium and a neutron.
Total the atomic numbers.
$1 + 1 = 2; \ 2 + 0 = 2$
Charge conserved.
Name the process.
$\text{big nucleus on the right: fusion}$
Two small ones joined.
Explain the difficulty.
$\text{both nuclei positive}$
Millions of degrees to overcome the repulsion.
Read the neutron yield.
$3 \text{ neutrons per split}$
From the uranium equation above.
Count the first generation.
$1 \to 3$
One split.
Count the second generation.
$3 \times 3 = 9$
Each neutron splits a nucleus.
Count the third generation.
$9 \times 3 = 27$
Multiplying, not adding.
Look ten generations on.
$3^{10} = 59\,049$
Uncontrolled growth.
Apply the control rods.
$\text{absorb all but one per split}$
Each generation then equals the last.
Read a steady reactor.
$1 \to 1 \to 1$
A chain held at exactly one.
Total the mass numbers.
$239 + 1 = 240; \ 144 + 94 + 2 = 240$
Count the free neutrons on both sides.
Total the atomic numbers.
$94 + 0 = 94; \ 56 + 38 + 0 = 94$
Neutrons carry no charge.
Name the process.
Match each kind of ionizing radiation to what it takes to stop it. One of the four answers offered is not true of any of them.
| a few millimetres of aluminum | several centimeters of lead, and even then it is reduced rather than stopped | a sheet of paper, or a few centimeters of air | nothing at all: it goes through everything without being weakened | |
|---|---|---|---|---|
| beta-minus | ||||
| gamma | ||||
| alpha |
Complete the worked solution: deuterium, mass number two and atomic number one, fuses with tritium, mass number three and atomic number one, giving a helium nucleus and one free neutron. Find the mass-number total on the left, the atomic-number total on the left, and the helium nucleus's mass number.
Total the left mass numbers.
$\text{two} + \text{three} =$ a
Deuterium and tritium.
Total the left atomic numbers.
$\text{one} + \text{one} =$ z
Helium's atomic number.
Find helium's mass number.
$(\text{left total}) - \text{one} =$ h
The neutron takes one away.
A university technician has written down how a sealed gamma source is to be used in a demonstration. Three of these four sentences keep a defense in place. Mark the one that gives two of them up at once.
This task has no paper form; do it on a device.
In plutonium-239 splitting in a reactor that has been running a long while, one neutron goes in and $2$ come out. Suppose every one of those goes on to split another nucleus of the same kind. How many neutrons come out of that second generation altogether?
Answer: neutrons
An industrial radiographer inspects pipeline welds in Texas with a sealed gamma source. At $1$ m the dose rate is $3600$ units per hour. What is it at $5$ m?
The answer: a units per hour.
Something is going on in the center of the Sun, and of every star like it. The equation for it is $\mathrm{^{1}_{1}H} + \mathrm{^{1}_{1}H} \rightarrow \mathrm{^{2}_{1}H} + \mathrm{^{0}_{+1}e} + \nu$, and the deuterium nucleus weighs slightly less than the two protons that made it. Which kind of nuclear change is this?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Here is uranium-235 coming apart a second way, because a nucleus does not split to order, which happens in the same core, a microsecond later and a different nucleus: $\mathrm{^{235}_{92}U} + \mathrm{^{1}_{0}n} \rightarrow \mathrm{^{140}_{55}Cs} + \mathrm{^{93}_{37}Rb} + 3\,\mathrm{^{1}_{0}n}$. Audit it. Total the mass numbers across everything on the left and everything on the right, then do the same with the atomic numbers.
| total on the left | total on the right | |
|---|---|---|
| mass number | ||
| atomic number |
You can audit a fission or fusion equation on both counts, name which process it is from the sizes, and say what time, distance and shielding each do. Tell someone why a reactor's spent fuel is a problem for decades for one reason and for thousands of years for another. That closes the nuclear unit, and with it the last of the twelve units of Chemistry 1.
15. Your turn: $\mathrm{^{239}_{94}Pu} + \mathrm{^{1}_{0}n} \rightarrow \mathrm{^{144}_{56}Ba} + \mathrm{^{94}_{38}Sr} + 2\,\mathrm{^{1}_{0}n}$. Does it balance, and which process is it?, step 3
$\text{big nucleus on the left: fission}$
It balances on both counts.