E2science

An atom of carbon 12 is made of six protons, six neutrons, and six electrons, which when added together have a mass of 12.095646 amu. But carbon 12 is defined as having an atomic weight of exactly 12.000000 — in fact this is the standard by which all other atomic weights are defined. How do we account for the extra 0.095646 amu?

This mass discrepancy is called the mass defect, and is one of the fundamental properties of nuclear physics. When nucleons come together to form an atomic nucleus, a fraction of their mass is lost as it is converted to energy and released as electromagnetic radiation. This is the source of the energy released in the fusion process, and must be supplied back to the nucleus in order to separate its components again. It is called, therefore, the binding energy that holds the atomic nucleus together. Binding energy can be found with Einstein's famous E=mc² equation after measuring the mass of the atom and comparing it to the mass of its component parts.

Up to a point, binding energy increases with atomic weight. Iron 56 is the element with the highest binding energy per nucleon (with a mass defect of 0.52872, more than half a proton!). Iron is therefore the largest atom which can be formed by a star's normal nuclear fusion process, because the formation of larger elements would not release energy, they require energy. In general, elements and isotopes above iron 56 can only be created by the awesome forces generated by a supernova, and even then only up to uranium. Elements with a higher atomic number are created by beta decay of uranium, or high energy nuclear physics experiments.

Calculating mass defect:
• Proton: 1.007277 amu
• Neutron: 1.008665 amu
• Electron: 0.000548597 amu
• 1 amu = 1.6606E-27 kg
• c = 299.792458E6 m/s²
• 1 Joule = 6.2415E12 MeV

Silicon 28 has an atomic weight of 27.9769271 amu, and is composed of 14 protons, 14 neutrons, and 14 electrons. Therefore, its mass defect is:

D_m = m_p + m_n+ m_e - m_atom
14(1.007277) + 14(1.008665) + 14(0.000548597) - 27.9769271 = 28.2308684 - 27.9769271 = 0.2539413 amu
or
421.6793638E-30 kg

Its binding energy is then:

E=mc²
(421.6793638E-30 kg)(299.8E6 m/s²)² = 3.78986512E-11 J
or
236.5448008 MeV

We see that 1 amu of mass defect is equal to 931.4908918 MeV, MeV being the standard unit of binding energy.

Sources:
http://www.tpub.com/content/doe/h1019v1/css/h1019v1_45.htm
http://www.colorado.edu/physics/2000/periodic_table/amu.html
http://www.cartage.org.lb/en/themes/Sciences/Chemistry/NuclearChemistry/NuclChemIndex/NuclearBindingEnergy/NuclearBindingEnergy.htm

Thanks to RPGeek for some corrections.

Lepton number is a conserved quantity in fundamental particle physics. As would be expected, this quantity is associated with the class of elementary particles called leptons: the electron, muon, and tau particles, and their corresponding neutrinos. All of these particles have lepton number +1, and their antiparticles have lepton number -1. All other Standard Model particles have lepton number 0.

Conservation of lepton number is obeyed by all known interactions, i.e. it is conserved absolutely. This has a significant effect on the nature of particle interactions and decays. Conservation of lepton number often prescribes the production of neutrinos and antineutrinos, since they have no charge and thus do not disturb the conservation of charge in an interaction. Two illustrative examples of conservation of lepton number are the decay of the pion and the decay of the neutron.

Examples

When a positive pion, π⁺, decays, it generally (99.99% of the time) decays into an antimuon, μ⁺. However, while an antimuon has lepton number -1, a pion has zero muon number. Thus the reaction π⁺ -> μ⁺ never occurs. Rather, we must add a muon neutrino, ν_μ, to the final state so that the lepton number of the final state is also zero. So lepton number conservation dictates that pion decay proceeds by the reaction: π⁺ -> μ⁺ + ν_μ

A free neutron will decay into a proton after an average lifetime of about 900 seconds. Conservation of charge requires that an electron also be produced, so that the final state is electrically neutral. This electron provides a lepton number of +1 to the final state, and since the initial state has lepton number 0, this requires an antilepton in the final state. A positron would destroy conservation of charge, so an antineutrino, ν_e, is the only option. This provides a lepton number of -1, balancing the final state and giving the final reaction: n -> p + e^- + ν_e

Both of these examples have the initial lepton number equal to 0, that is, they're hadron decays. An example with nonzero initial lepton number is electron capture by a proton in a nucleus, which is a form of inverse beta decay. Here, a proton absorbs an electron to become a neutron. To conserve lepton number, there must also be a particle in the final state with lepton number +1, i.e. a neutrino. So the reaction for electron capture is p + e^- -> n + ν_e

True Structure of the Lepton Number

Lepton number, it turns out, is not actually a basic physical quantity but the sum of three quantities corresponding to the three 'generations' of leptons. These quantities are electron number, muon number, and tau number. Each particle in a given generation has its lepton number due to the corresponding lepton family number (e.g. the electron has +1 electron number and 0 muon and tau number). Each of these quantities is conserved separately, although neutrino oscillation violates the conservation of lepton family numbers. This explains the choices of neutrino type in the above reactions.

This separate conservation of lepton numbers is evident in muon decay. Muons decay into electrons, and if only conservation of total lepton number is considered, the decay μ^- -> e^- would appear to be possible, as the lepton number of both sides is +1. However, this is not the case, as the muon number of the initial state is +1 and the muon number of the final state is 0. To fully conserve lepton numbers, two neutrinos must be emitted, a muon neutrino and an electron antineutrino. Then, not only is the total lepton number conserved, but so are the electron number and muon number. The reaction is thus μ^- -> e^- + ν_e + ν_μ

Summary

Lepton number conservation is an important symmetry of the Standard Model of particle physics. It, along with the other conservation laws of the standard model, specifies the form of particle interactions at the fundamental level. Unlike many other conservation laws in the Standard Model, lepton number is conserved absolutely, i.e. no lepton-number violating interactions have ever been observed. Neutrino oscillation violates the conservation of the separate lepton family numbers, but at a low enough level such that the probability of lepton family violation in other reactions may be unobservably small. Searches for lepton number violating interactions are ongoing, as they would be signs of physics beyond the standard model.

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Sources include my senior undergraduate particle physics course and the (very technical) Particle Data Group website at http://pdg.lbl.gov/

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(CC)
This writeup is copyright 2004 D.G. Roberge and is released under the Creative Commons Attribution-NoDerivs-NonCommercial licence. Details can be found at http://creativecommons.org/licenses/by-nd-nc/2.0/ .

Anyone who has ever eaten an apple has probably noticed that by the time you’re nearly finished and come back around to where you took your first bite, that part of the apple has started to turn brown. Why? Toasting bread turns it brown; frying potatoes turns them brown; a few days after Hallowe’en your pumpkin will start to turn brown. Why?

It turns out, there’s a number of reasons why foods turn brown:

Caramelization
Caramelization occurs when a sugar is heated to a high temperature, over 248°F (120°C). At these temperatures the sugar undergoes a process called thermal degradation and breaks down into two compounds: one, which provides the caramel aroma, and a residue that creates the familiar brown colouring.

The process of camelizing sugar is complex and there are a number of different flavours and colours that can be produced depending on the acidity of the sugar compound, the heat used and the duration the sugar is heated.

Maillard Reactions
This reaction is named after the French scientist, Louis Camille Maillard, who discovered it in 1912. It occurs when a carbohydrate (such as sugar) reacts with a protein at high temperatures. More specifically, the aldehydes in the sugar molecule react with the nitrogen (amino acids) in the protein, to produce melanoids, which in turn produce the flavours associated with the process.

Enzymatic browning
And now we come back to the apple. Enzymatic browning, or oxidation, doesn’t require heat and generally isn’t used to enhance the flavour of food, although the flavour of some foods like tea and coffee are enhanced by controlled enzymatic browning.

This type of browning occurs in fruits like apples and bananas, vegetables like potatoes, and seafood like shrimp. A chemical reaction takes place between the enzymes (polyphenol oxidase or tyrosinase) in the food and the oxygen in the air, producing melanins. The process damages the cells of the food and changes the colour and flavour.

In fruit and vegetables, the skin of the food prevents oxidation but it will brown quickly once cut. When cut, the damaged cells release the enzymes and react with the air. Bruised fruit will also turn brown since the damaged cells in the bruise will react with the air in the food.

Removing the enzymes before they have a chance to react with the air can control enzymatic browning. For example, blanching (boiling in water for a short time) will prevent fresh shrimp from browning.

The reaction can also be prevented by not allowing the food to come in contact with oxygen. Ever notice that when your Mom is cutting potatoes, she puts them directly into a pot of water rather than letting them sit in an open bowl? There’s less oxygen in the water. Apples can be stored for months at a time by flooding the storage container with carbon dioxide and displacing the oxygen.

Carmelization and Maillard Reactions are also referred to as non-enzymatic browning.


Sources
http://www.scienceyear.com/outthere/index.html?page=/outthere/diner/why/browning.html
http://www.geocities.com/perfectapple/brown.html
http://www.exploratorium.edu/cooking/candy/caramels-story.html
http://www.agsci.ubc.ca/courses/fnh/410/colour/3_81.htm

Plasma balls are pretty demonstrations of plasma. The research group I'm part of uses a flat one to attract new students. Like a lava lamp or a fire, the constantly changing pattern is something that can capture your attention for a long time. If you look at it, you can see a small central ball, from which luminous threads emanate to an outer glass ball.

So, how does it work? A detailed description of this device would be a good subject for a PhD thesis rather than a node, so this will be a rough description only.

The plasma is generated by a high-voltage (several kV) high-frequency (several kHz) power supply, that uses the small central ball as an antenna. Because the voltage is so high, free electrons in the gas surrounding the central ball get very high energies, so high that they can excite and ionize the gas. This ionization produces more electrons, which help to sustain the plasma.

The excited species are basically gas atoms from which one of the outer electrons is kicked into an higher orbit, which is at a higher energy level. It will stay in this higher orbit for a very short time, say a few nanoseconds to a few microseconds. It will then fall back to a lower orbit, emitting the excess energy as photons — light. Because atoms have discrete energy levels, the photons emitted also have discrete energies, causing the light emitted by the plasma ball to have discrete colours.

Various gases can be used to create the plasma in. Because every gas has different energy levels, each gas will give a different colour of light. Some popular gases are:

• Helium: brilliant white
• Neon: red, with orange ends
• Argon: lavender
• Krypton: white
• Xenon: bluish white
• Nitrogen: orange
• Carbon dioxide: white or blue

Oxygen or water are bad news for the plasma ball, as the electronegative oxygen will gobble up electrons, making discharges very weak. It is possible to create threads, or streamers (They are not arcs, arcs are something entirely different!) as plasma physicists call them, with various colours using a mixture of gases. Because the electric field gets weaker near the glass, the electrons collisions are likely to have less energy there than in the center. If you put in a gas with a smaller energy distance between atomic levels and one with larger distance between energy levels, you can get the plasma to excite the former near the wall and the latter near the center, giving you a nice multicoloured streamer.

The gas in the plasma ball is at subatmospheric pressure, usually around one kPa. The reason why you don't want too high a gas pressure is that in that case, electrons collide so often that they haven't gained enough energy between collisions to excite or ionize the gas, which is bad for the discharge. If the pressure is too low on the other hand, the electrons will collide less often, also diminishing the strength of the discharge. This leads to an optimum of the ratio of electric field and pressure. This effect is expressed in a Pashen curve, which is different for each gas or mixture of gases. Home builders often use atmospheric pressure and a much higher voltage to compensate.

The glass sphere surrounding the gas acts as a return circuit. While glass is obviously an isolator, the high-frequency electric field can travel over the surface of the globe, closing the current loop. However, if you touch the globe, your body, which is a very good conductor of high-frequency electric current, will act as a return path, causing most of the pretty plasma streamers to collect near your hand.

Why the plasma organizes in streamers, rather than in a homogeneous glow is a difficult matter. A key mechanism is however the tendency of current to seek the path of the least resistance. If a piece of plasma is more ionized than the pieces of plasma around it, it has a lower restance. This will draw more current in, further increasing the ionization. This is a self-amplifying mechanism, causing the plasma to organize in discrete streamers.


Sources: I got the list of plasma colours off http://www.egglescliffe.org.uk/physics/fun/plasma/plasma.html at July 10th 2004.

Space is very cold-on average, about 3 K. So, how come our astronauts do not freeze to death?

On Earth, heat transport is mostly done by conduction of heat through a substance, and convection. Both of these transport mechanisms however depend on the presence of mass to do their heat transport, something in which space is sorely lacking-typical densities are perhaps a few dozen atoms per cubic meter. Compare this to 10²⁵ per cubic meter for air, and you quickly see that even though space is on average 3 K, you still won't have a lot of cooling from this. To get a nice demonstration of this phenomenon, try the difference between licking 0-degree air, and a 0-degree metal bar*.

No, astronauts lose their heat mainly through blackbody radiation. It so happens that this process can be simply described by the Stefan-Boltzmann law:

Φ=(1-ε) σ T⁴

Here, Φ is the radiative flux, ε is the albedo, or whiteness, and σ is the Stefan-Boltzmann constant, numerical value 5.67x10^-8 J K^-4 m^-2 m^-1. By integrating the flux over the area of his space suit we can now compute the amount of heat he loses by radiation.

Now, we'll use some reasonable numbers to get a rough idea how much heat our astronaut loses. His space suit has an area of about 2 square meters. It's white, so the albedo is high, say 0.9. The temperature of our astronaut is 310 K, or body temperature. This gives a power output of 100 W, which is close to the power your average human puts out.

The T⁴ has another neat implication: if the power varies by a factor of 2, the temperature will only vary by a factor of 1.19. So, you can change the power by quite a bit, while only varying the temperature by a modest amount. Say our astronaut gets very active, and his power becomes 50 percent higher. The temperature will eventually become 343 K, or 70 C. However, with the isolating properties and heat capacity of the spacesuit he's likely to be fine.

There is however one large assumption made in this whole story: that space doesn't radiate back. This is all fine if you consider only the background radiation of 3 K, which will contribute a measly 0.9 microwatt in our example. However, if the astronaut gets into the sun, without protection, it becomes a different story. I won't do the maths, but suffice it so say the sun heats the earth up to an average temperature close the body temperature of our aforementioned astronaut, so this amount of heat is definitely not negligible. I imagine it will get sweaty in there.

As a final remark, you might have wondered why the power dissipation of suit and astronaut match so closely. I mean, why would the Stefan-Boltzmann constant have a value that allows a human to survive in space? Before you start blaming your favorite deity, let me point out that there is one parameter that we have control about: the albedo. By setting it high, we put the dissipation at a comfortable value. If we were to paint the suit black, the albedo would be higher, so there would be more blackbody radiation. This would mean it would become quite chilly for our astronaut. In short, spacesuits are white because space is cold. As a bonus, the white color reflects the sunlight, so the astronaut is less likely to get baked.

Sources:

• http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html
• http://scienceworld.wolfram.com/physics/Stefan-BoltzmannConstant.html
• m_turner made a good point about the sun being reflected of the spacesuit, and about me mixing up Nernst coeffient and albedo.

*Disclaimer: This will likely cost you your tongue. So, actually, you'd better not do this and just believe me.