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Chapter 34: Problem 2

Why is a chain reaction more likely to occur in a big piece of uranium than in a small piece?

Short Answer

Expert verified
A chain reaction is more likely to occur in a big piece of uranium than in a small piece because the larger volume provides more opportunity for fission-causing neutrons to encounter other nuclei and the lower surface area-to-volume ratio reduces the chance of neutrons escaping.

Step by step solution

01

Understanding Chain Reaction

A chain reaction in nuclear physics refers to a series of nuclear fissions (splitting of atomic nuclei), each initiated by a neutron produced in a preceding fission. For a sustained chain reaction, there must be a critical mass of the fissile material, which depends on its size, shape, and purity, among other factors.
02

Considering Escape Probabilities

In a big piece of uranium, there is a higher probability that neutrons from a fission event will encounter other uranium nuclei to continue the chain reaction, because there is a larger volume of fissile material. The likelihood that neutrons escape without causing further fissions is lower than in a small piece of uranium.
03

Reflecting on Surface Area to Volume Ratios

A big piece of uranium has a smaller surface area to volume ratio compared to a small piece. This means that a larger proportion of neutiles produced in fission events within a large piece of uranium are likely to strike other fissile nuclei rather than escape, making the chain reaction more likely to be sustained.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nuclear Fission
Nuclear fission is the process that powers the sun and gives us nuclear energy. It happens when the nucleus of an atom, like uranium or plutonium, breaks apart into two smaller nuclei. This split releases a lot of energy and also frees more neutrons.

Think of it as a cosmic game of pool: when the nucleus splits, the freed neutrons can go on to hit other uranium atoms, causing them to split too. If this keeps happening, we get what鈥檚 called a chain reaction, kind of like continuously breaking up the rack of pool balls with every shot.
Critical Mass
To keep the nuclear 'pool game' going, we need enough uranium in one place; this amount is what scientists call the 'critical mass.' It's the smallest amount of fissile material needed to keep the chain reaction self-sustaining. If you have less than this critical mass, the reaction peters out because too many neutrons escape into the aether instead of hitting other uranium atoms.

So, if you want to start a nuclear fission party and keep it going, you better make sure you have enough fissile friends to dance with鈥攖hat's your critical mass.
Fissile Material
Fissile materials are the VIP guests at the nuclear fission party. They're special types of atoms, like uranium-235 or plutonium-239, that can actually sustain a chain reaction. These materials are super picky: you hit them with a neutron, and they'll only split if the neutron is just the right speed.

It's like fissile materials won't dance unless the DJ plays their favorite song at the perfect volume. If you have a bunch of these fissile atoms together and you get them to start 'dancing' (splitting), you've got the makings of a powerful reaction on your hands.
Neutron Behavior
Neutrons are the life of the nuclear party鈥攖he movers and shakers that keep the energy flowing. After a nucleus splits, these freshly released neutrons skedaddle at high speeds, seeking other nuclei to strike. Picture them as high-energy guests bouncing from conversation to conversation, igniting discussions (fissions) wherever they go.

If they exit the party early (escape the fissile mass), the energy dips, and the reaction slows down. But if they stick around and keep mixing, the party keeps hopping鈥攖hat's the essence of a sustained chain reaction.
Surface Area to Volume Ratio
The surface area to volume ratio is like the layout of the party venue; it determines how easy it is for guests (neutrons) to leave early. A big piece of fissile material is like a massive party hall: there's more space for interactions than exits, meaning neutrons are more likely to bump into someone and keep the chain reaction going.

In contrast, a small piece has more doors (surface area) compared to its size (volume), so it's easier for neutrons to split without contributing to the fission fiesta. To really get things fizzing, go for a grand ballroom鈥攍arge volume with relatively fewer exits.

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Most popular questions from this chapter

Oxygen and hydrogen atoms combine to form water. If all three nuclei in a water molecule were fused, what element would be produced?

Do today鈥檚 nuclear power plants use fission, fusion, or both?

In a nuclear fission reaction, which has more mass: the initial uranium or its products?

What were the two methods used to separate U-235 from U-238 in the Manhattan Project during World War II?

The kiloton, which is used to measure the energy released in an atomic explosion, is equal to \(4.2 \times 10^{12} \mathrm{J}\) (approximately the energy released in the explosion of 1000 tons of TNT). Recalling that 1 kilocalorie of energy raises the temperature of 1 \(\mathrm{kg}\) of water by \(1^{\circ} \mathrm{C}\) and that 4184 joules is equal to 1 kilocalorie, show that the energy released by a 20 -kiloton bomb is enough to heat \(4.0 \times 10^{8}\) kilograms of water (nearly half a million tons) through \(50^{\circ} \mathrm{C} .\)
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