27 Sept Class Summary

8.15 AM, August 6, 1945 and 11.01 AM, August 9, 1945. These are the times when “Little Boy” and “Fat Man” were dropped and mother Earth loses her children, Hiroshima and Nagasaki.

Fact 1: Hundreds of thousands of lives were lost.

Fact 2: Mankind is to blame.

Nuclear technology, like any other technology comes from ideas generated by human brains. How these brains decide of its usage is what determines which path it’s going to undertake. History remains, but not forever the same and instead of fearing, let us now benefit from it.

Electricity generated from a nuclear power plant can be used for so many goods. From ensuring a life-support machine operates in keeping an old life, to medical equipments needed in welcoming the birth of new ones.

So how does nuclear technology works?

People, I would like you to meet Mr Atom. You can’t see him mainly because of his 10^-8­ cm size but just bear in mind that he’s there and very real. Now, Mr Atom has this multiple personality disorder: Mr Protons, Mr Neutrons and for some very disturbing reason, Ms Electrons. Mr Protons is a very positive person (very nice guy) whilst Ms Electrons is unreasonably negative (handful!) Mr Neutrons on the other hand, well let’s just say he’s tive-less.

Do not however be deceived by his tininess cause this guy can sure give you a run for your money. Permit me to be Einstein for a moment. From [1]:

You see, E = mc² (duh!)

where E is energy, m is mass and c is the speed of light (approximately 300,000 kilometers per second). You may have heard of this equation without knowing what it means but really the concept behind it is pretty simple. Matter and energy are essentially interchangeable -- matter can be converted into energy, and vice-versa and the numbers involved are enormous. The speed of light is a huge number -- if you multiply a large amount of mass by the speed of light, you get an extreme amount of energy. And atoms are small (duly noted) -- they don't have a lot of mass (again, duly noted) -- so it takes a vast number of them to make a substance. (I give!)

Substances like uranium, which are commonly used in nuclear bombs, have a very high atomic number -- the atoms themselves are larger and contain more particles than the atoms of other naturally-occurring substances. Because of this additional nuclear material, uranium has the power to release a lot of energy. If you multiplied 7 kilograms of uranium by the speed of light squared, you would get about 2.1 billion Joules of energy. By comparison, a 60-watt light bulb uses 60 joules of energy per second. The energy found in a pound of highly enriched uranium is equal to something on the order of a million gallons of gasoline. When you consider that a pound of uranium is smaller than a baseball and a million gallons of gasoline would fill a cube that is 50 feet per side (50 feet is as tall as a five-story building), you can get an idea of the amount of energy available in just a little bit of U-235 (go figure!)

You might wonder why fission bombs use uranium-235 as fuel. Uranium is the heaviest naturally occurring element on Earth, and it has two isotopes - uranium-238 and uranium-235, both of which are barely stable. Both isotopes also have an unusually large number of neutrons. Although ordinary uranium will always have 92 protons, U-238 has 146 neutrons, while U-235 has 143 neutrons. Both isotopes of uranium are radioactive, and they eventually decay over time. U-235, however, has an extra property that makes it useful for both nuclear-power production and nuclear-bomb production -- U-235 is one of the few materials that can undergo induced fission. Instead of waiting more than 700 million years for uranium to naturally decay, the element can be broken down much faster if a neutron runs into a U-235 nucleus. The nucleus will absorb the neutron without hesitation, become unstable and split immediately.

This figure :



 
shows a uranium-235 nucleus with a neutron approaching from the top. As soon as the nucleus captures the neutron, it splits into two lighter atoms and throws off two or three new neutrons (the number of ejected neutrons depends on how the U-235 atom happens to split). The two new atoms then emit gamma radiation as they settle into their new states. There are a couple of things about this induced fission process that makes it interesting:

• The probability of a U-235 atom capturing a neutron as it passes by is fairly high. In a bomb that is working properly, more than one neutron ejected from each fission causes another fission to occur. It helps to think of a big circle of marbles as the protons and neutrons of an atom. If you shoot one marble -- a single neutron -- in the middle of the big circle, it will hit one marble, which will hit a few more marbles, and so on until a chain reaction continues (getting any urges to play pool?
• The process of capturing the neutron and splitting happens very quickly, on the order of picoseconds (0.000000000001 (now that’s a tongue twister!) seconds).

Reactivity plays a major role in how much power being generated. What’s reactivity you ask? Reactivity is a measure of the departure of a reactor from criticality. Say what? Okay, it breaks down to these:

·         There’s a nuclear reactor

·         If the population of neutrons inside that reactor remains relatively constant, we say it has achieved criticality.

ρ = k_eff  - 1

Reactivity (ρ) determines whether a reactor is critical. The effective neutron multiplication factor, k_eff is the average number of neutrons from one fission that causes another fission. The remaining neutrons either are absorbed in non-fission reactions or leave the system without being absorbed:

·         (k_eff = 1) : Every fission causes an average of one more fission, leading to a fission (and power) level that is constant. Nuclear power plants operate with k = 1 unless the power level is being increased or decreased

·         subcritical (k_eff < 1) : The system cannot sustain a chain reaction, and any beginning of a chain reaction dies out over time. For every fission that is induced in the system, an average total of 1/(1 − k) fissions occur.

·         or supercritical (k_eff > 1) : For every fission in the material, it is likely that there will be "k" fissions after the next mean generation time. The result is that the number of fission reactions increases exponentially, according to the equation

e^{(k − 1)t / Λ}, where t is the elapsed time. Nuclear weapons are designed to operate under this state.

How do we control criticality of a power plant you ask? (boy, aren’t you inquisitive) By using control rods to effectively absorb neutrons and by changing the position of these rods in the core, we can change the status of a reactor’s criticality.

Reactivity affects the multiplication of neutrons and consequently the power of the reactor. The speed of changes of the power level is the factor that determines whether it is easy or difficult to regulate a reactor.

From n_N = n₀e^NΔk (1) we get P = P₀e^NΔk (2)

Where

·         n_N : number of neutrons in N generation

·         N : number of generations

·         Δk : multiplication factor

·         n₀ : initial number of neutrons

·         P : total power

·         P₀ : initial power

However, knowing the change in power relative to the number of generations alone is not enough. Why? Because the deciding factor in how fast the neutrons multiply is the lasting length of neutron generation, which is why the above equations need to be with respect to time.

The time (t) required for N generation is t = l · N (3)

Where l is the neutron’s life-time (time-span between generations). Substituting (3) into (2) gives

            P(t) = P₀e^Δkt/l

We can conclude that the larger Δk is and smaller l is, the faster the neutrons multiply and the faster the power level will increase over the course of time. There are two important things to note though namely:

·         Δk or ρ are quantities controlled by the regulation system and can be modified within reasonable limits

·         Neutron life-time, l is a quantity that depends on the reactor and cannot be modified at will

Now, let’s have a look at prompt and delayed neutrons. In the fission of ²³⁵U, about 99.35% of neutrons produced are prompt whilst the remaining 0.65% are delayed neutrons. Even though only a small portion of delayed neutrons are represented, increased it has of average neutron life-time of all neutrons. If all neutrons were prompt, the speed at which power level increases would be at an immeasurable level of fastness (imagine Road Runner minus the annoying beep). This would result in an impossible control of the reactor since the power changes are occurring too fast. We would also be facing serious problem with the emergency systems (mayday! mayday!)  since the fastest protection system requires about a second to be effective and during this lapse, severe damage could be caused by the excessive power levels reached. 


So,  we've reached the end of our first entry and I'm sure (well hoped actually) that you've all gained useful info from this. Comments and suggestions are greatly appreciated (so leave them!) See you tomorrow. :)

P/S : Like and recommend us please huhu

reference:

• nuclear bomb [1]
• criticality
• hiroshima and nagasaki