A matrix means something that has something else regularly embedded within it. For example, a snickers bar has a matrix of caramel and nuts - the nuts are embedded in the caramel. Or we could say that the caramel is impregnated with nuts (these are the actual terms used). Most rocks are matrices because they are mostly one type of mineral, with smaller crystals of another type embedded within them. Note, in mathematics, a matrix is a 2D number grid that has specific rules for doing calculations, but it still means a grid impregnated with numbers.
Attenuating just means "getting thinner", like a wedge. So an attentuating matrix means a lump of stuff, that has something regularly embedded in it, which is thin at one edge but gradually gets thicker to the other.
In 1945 the allied forces dropped two nuclear warheads on the Japanese cities of Hiroshima and Nagasaki. Today, both cities are not only rebuilt but populated. By contrast, the Chernobyl accident which occured in 1985 led to an exclusion zone which is still heavily patrolled; Chernobyl is still radioactive while Hiroshima and Nagasake are not. How come?
What's really worth mentioning here is that nobody actually has a clue what happens to the world in long term after a nuclear event. Because it doesn't happen very often, all the claims you hear about "this place will stay radioactive for 40,000 years" are really just hypotheses because nobody is 100% sure. But here's what we do know.
When Little Boy (the Hiroshima bomb) detonated, around 0.9 kilograms of nuclear fuel was actually activated, enough to destroy a city but not a huge amount of actual stuff. By contrast, Chernobyl was not a nuclear explosion. It was actually a steam explosion that happened inside a nuclear reactor. There was no fire, but a huge steam-blast scattered all the nuclear fuel and nuclear waste into the Pripyat area. In other words, the Hiroshima bomb activated and used up its nuclear fuel in the blast, while the Chernobyl event covered the area in un-reacted nuclear fuel i.e. stuff which still contains its nuclear energy.
The specifics are quite complex because it relates to the different types of atom being turned into other types of atom but the way to think of it is that Hiroshima used up most of its "dangerousness" in the blast while Chernobyl just seeded the land with dangerous stuff, still ready to poison you!
Furthermore, the amount of nuclear fuel at Chernobyl was closer to 163,000 kilograms (rather than the meagre 0.9 of Hiroshima). Although Hiroshima might seem like a more terrifying event, Chernobyl involved a much larger amount of nuclear material. So it's like the difference between quickly blowing up one piece of coal (looks more spectacular but it's not a huge amount of fuel) as opposed to taking a mountain of coal and gradually burning it slowly for many years (looks less impressive but it's going to last longer).
The other main factor to consider is that both the Hiroshima and Nagasaki bombs were actually detonated mid-air, meaning that a lot of the nuclear material was blown and scattered around by the wind. Over time, it was carried away and diluted until both cities returned to normal background levels. By contrast, the Chernobyl event happened on the ground and a lot of the nuclear material was sprayed around the local area and went into the rivers, plants, soil etc. This means a lot of the nuclear material is still there, in the ground and in the water.
It's worth noting that a lot of animals are living in the abandoned Chernobyl site and honestly, nobody's quite sure why. It's possible that people have overestimated the effects of radiation exposure, perhaps the world's ecosystems have a way of taking care of themselves we don't know about or, maybe, a lot of these animals have somehow developed some advantageous mutation which makes them less susceptible to radiation poisoning (probably unlikely, but at the moment, we have to consider any plausible hypothesis).
Our sun falls into a classification of star called a "yellow dwarf". It's a fairly small Sun and burns at a pretty middle-of-the-range temperature. In fact there's nothing remarkable or rare or unusual about our Sun at all!
The shape and size it has depends on two factors: the heat from the core's nuclear fusion reacion pushes everything out and the gravitational pull from the core pulls everything in. These two effects (heat out, gravity in) gives the star its size and spherical shape.
In around 4.5 billion years (the sun is halfway through its lifetime) the Sun is going to change. The Sun's main fuel source is Hydrogen, but that will run out and the core will gradually start to shrink. As it shrinks this will concentrate its heat making it hotter, so the "outward" force will start to increase, gradually overpowering its current gravitational pull. The Sun will slowly begin to swell, getting larger and larger as the heat rises.
By 5 billion years time, the heat from the condensed core will be so great that the Sun will have expanded to swallow the inner planets, including the Earth. It will then have changed its classification to what we call a "red giant". Once this happens the Earth is doomed. If we plan on surviving as a species, we're going to have to get going!
A musical note is a vibration in the air at a constant speed. 440 vibrations per second, for instance, is what musicians call "middle C". But if you play middle C on a piano it sounds different to if you play it on a violin or a recorder or a set of bagpipes. Musicians refer to this "texture" the musical note has as the timbre (pronounced tom-bruh) and it's the french word for "sound quality". The reason different instruments produce a different timbre is because when a musical instrument plays a note, it isn't playing JUST that note.
A piano, when you press middle C, is vibrating a string inside it at 440 vib per sec, but it's also, at a slightly lower amplitude playing 880 vib per sec. This higher version of the same note is a called a "harmonic" of the initial frequency. Not only that, but the vibrating air inside the piano is bouncing off the walls of the piano, interfering with other strings and playing the notes either side of it a little bit, for instance playing 293.7 (middle D). The main note you hear is 440, but this is combined with other notes called "overtones". The combination of overtones, harmonics and the original note together are what produce the different sound quality of an instrument.
If you use a signal generator you can create a "pure" note; the kind you might have heard your Physics teacher generating with a speaker. It sounds electronic. But if you add in overtones and harmonics at different amplitudes you can simulate the sounds of other instruments (which is how synthesisers do it). So, different sound quality is all about mathematics: combine the right frequencies in the right order and the right amplitudes and you can simulate anything from a Cello playing a B flat, to a Giraffe sneezing!
If you've studied quantum field theory in any depth you'll have probably come across the idea of a Planck time (sometimes called a planck second). It's 5.4 x 10^-44 seconds and it's a very interesting chunk of time because it's the point at which our laws of physics break down. By that what I mean (roughly) is that if you take Gravity, the energy per frequency of the Universe and the Universal speed limit, it is possible to juggle the terms around so that you end up with a very small distance called the Planck length (1.6 x 10^-36 meters). This length is a mysterious value and we can calculate the amount of time it would take for the fastest thing in the Universe (light) to cross it, giving us the Planck time.
The question really is, where does this number come from and does it have any significance. Here's what we know for definite. The laws of Physics including General Relativity and Quantum Field Theory (the two main branches of what I like to think of as "deep Physics") definitely work on lengths greater than the PL and on timescales longer than the PT. And that's about as much as I can honestly say.
When we drop below these values and talk about shorter distances and shorter times it isn't actually clear that the normal rules of Physics apply. The Planck scales represent the current limit of our understanding so it's very hard to speculate about what goes on beyond them. Some have suggested that these numbers are arbitrary; that they simply appear without any meaning. As if we took the mass of the Pacific Ocean and divideed it by the mass of the Atlantic and called the answer "The Ocean constant". It would be a definit answer, but it might be physically meaningless. Likewise the equation which gives us the Planck units might just be humans putting the main constants together and going voila, there's a number that unifies everything.
On the other hand it's possible that this number really does mean something, making it a fundamental property of the Universe that events cannot happen under the PT and objects separated by less than the PL are indistinguishable. It's possible that time is granular, just like distance. We know that energy only exchanges/exists in discrete chunks so we have to take the possibility that time and space could be the same extremely seriously. But, until we have a working theory of quantum gravity, we just don't know if the laws of Physics stop at the Planck scale, or whether they carry on and we'd just made these numbers up!
The question is whether the difference between two temperature readings relates to a direct increase in energy or some sort of exponential one. For example, 11 degrees C is 1 degree hotter than 10 degrees C, how much of an energy change is this and how would this relate to 12 degrees etc. It's an interesting question but when we get our terms absolutely defined, the question disappears sadly. The reason is that energy and temperature are not related exclusively. By that I mean that two objects at the same temperature can have different energies.
The amount of energy required to heat a system can be defined as the mass of the object being heated, multiplied by the temperature change, multiplied by "the specific heat capacity" which is a measure of how much energy an object can absorb in the process of changing temperature. Thing is, this equation is dependent on mass. In other words I could have a 1 g block of ice and apply a certain amount of energy to it. A 1000 g block of ice given the same energy will not raise its temperature anywhere near as much. So temperature and heat energy, while related, don't have a simple conversion factor because it depends how much stuff you're heating and what substance you're heating.
Smells and fragrances work because tiny molecules from the object we're detecting get released into the air and carried into our nose. Tiny little receptors up near the back of the nostrils recieve these molecules as an input and send an electric signal to our brain which we interpret as smell. Now it turns out that charcoal is particularly good at absorbing these smells (in fact Buck Weimer has even begun marketing clothes containing charcoal to absorb unpleasant biological smells). But how does it work?
The answer is that charcoal has a huge surface area. Although a lump of charcoal looks like one little piece, if you zoom in the surface of a charcoal lump is filled with holes, tubes and craters (it is, after all, based on plant matter) which means a single gram of charcoal can have several square meters of surface area, all wrapped up into a tiny lump. Invisible to the naked eye, but a small molecule can easily navigate them.
The next effect is that two objects naturally cling to each other. What's called the London force effect (or, to give it its older name: the Van der Waals effect) two particles will naturally cling to each other because of the temporary charges dancing around on their surfaces. We don't notice this effect most of the time because it's very subtle. A marble on a table is easily picked up by the human hand, but we actually have to overcome a nanoscopic London force to separate it from the table. What this means is that small objects will cling to each other very, very well.
So charcoal works by having a lot of surface area, which small particles go colliding around on. This constant interacting between the charcoal's surface and the tiny particles leads to an overall "stickiness" to charcaol. Kind of like if we were to throw a dozen balls into a hedge, a lot of them would get caught up and tangled on the branches. Thus, charcoal (or anything with a large surface area) can absorb smells!
Mars has a composition very similar to Earth's. The surface is primarily made from Iron (III) Oxide which on Earth we usually call "rust". The rocks on the surface are otherwise quite similat to the types found on Earth. Most rocks are made from metal bonded to non metals like carbon, silicon, phosphorus and oxygen and this is exactly what we find on Mars. Mars has crystals the same we way do and it also has deposits of pure metals like Iron, much the same as Earth.
Where MArs is different to Earth is in the atmosphere and at the poles. Whereas our air is mostly Nitrogen with some oxygen and less than 1% Carbon dioxide (with the polar caps made of water), Mars' atmosphere is made of around 95% Carbon dioxide with some Nitrogen thrown in (the polar ice caps being made of solid Carbon dioxide).
We have also, of course, recently discovered liquid water on the surface of the planet, which means that Martian soil could support bacterial or even plant life similar to Earth's, but the air would make it unbreathable for Earth animals. The fact that there's virtually no oxygen in the air suggests there aren't any plants undergoing photosynthesis there however, so if we were to find cellular life there it would be very different in behaviour and chemistry to Earth life.
I've just started the topic of esters and esterification with my year 12s so this is fresh in my mind. An esterification reaction is where a carbon-based acid and an alcohol react together to produce an ester (a particularly fragrant and pleasant smelling chemical). Normally this reaction needs acidic conditions and heat to work. Sam's question is, would stomach acid and body temperature be enough to get the reaction going?
The first thing to point out is that most alcohols are completely toxic to humans (technically so is the ethanol in alcoholic drinks). But the main alcohols humans can safely consume are ethanol and methyl butanol, most others would be poisonous. Acids however are pretty common in our diet and there's a wide range your mouth and stomach can take.
Stomach acid can be as concentrated as pH 1.5 which is definitely enough to catalyse the reaction, the question is really about the body temperature of a human (37 degrees Celsius normally), could this be enough to get an esterification going? The answer seems to be a definite yes. There are lots of esterification reactions known to take place between room and body temperature so it's absolutely feasible to do the reaction in your stomach.
The problem is: your stomach has a lot of water in it, and water tends to break esters down. However they wouldn't reverse the reaction completely. What you'd end up would be a dynamic system where esters are constantly being made, and constantly being un-made until we reach a balance where they're being made as fast as they're being created. We call this a dynamic equilibrium. In this equilibrium, the amount of ester would probably be quite low as there's a lot more water in your stomach than ingredients (if you've outdone your own stomach capacity with alcohol and carbon based acid you need to see a doctor...and then a psychiatrist) but it is absolutely plausible to carry out esterifications in your stomach.
This is an excellent question and it's one which very rarely gets asked. Energy is a notoriously difficult thing to teach because a lot of people (even Scientists) are taught it incorrectly in the first place, so they pass on a faulty explanation to their students.
Let me start by saying what energy is not. It's not a substance. When an object "gains energy" this does not mean it's somehow got more stuff to it. An object higher up has gravitational potential energy, this doesn't mean you could somehow look at it and count the "energons".
Energy, defined as simply as possible, is "the ability to do work". Work means Force x distance moved in direction of Force. Force is a mass changing its velocity and velocity is a description of what something is doing. So, going backwards, Force is a measure of making something change what it's doing. Work is a measure of how much we've changed the thing, and Energy is a measure of the ability to do that.
If this sounds a bit abstract then it should. Energy is an abstract concept and we don't need it for any explanation. Ever. Unfortunately people use the term energy so often that they stop thinking about what it actually means and say things like "this happened because of Energy" or "Energy is what made it happen". This is cheating. Besides being a misuse of the word Energy.
For example, we might refer to fuel being burned, releasing its energy, making the car go. But this is not an explanation. This is like saying "the thing which makes the car go, is what makes it go". The thing making the car go is the movement of the particles and their collisions with the interior of the engine block.
The fuel particles are vibrating around a lot as they smash into each other. As the particles bump into the inside of the engine, the electrons in one atom repel the electrons in the other atom causing an overall repulsive effect, pushing the engine (and anything attached to it) forward, and the reacted fuel particles backward.
The question is how much fuel will lead to how much movement? This is what we use Energy for. We can measure the fuel's potential to react as its chemical energy. We can measure its speed using kinetic energy. We can measure the interactions between the colliding atoms as electromagnetic energy and so on. So, if we have (for each part of the process) an equation which translates the actual thing happening into a common unit (the Joule) we can easily move back and forth from process to process. The actual events happening are the particles moving and interacting, not "Energy being released" or "Energy changing form".
Energy should not, strictly speaking, be used as a noun. It should be used as an adjective because it is a measurement/description of something. Any time we talk about Energy in a Scientific concept, we have to remember that we need to qualify what the energy relates to. To say "this particle has energy" is meaningless. To say "this particle has kinetic energy" or "this particle contains a certain number of potential photons" is meaningful.
What Energy actually is, is a useful way of keeping track of cause and effect. It's a physicists way of quantifying "how much of this cause" will lead to "how much of this effect". In Einstein's infamous E=mc^2 formula, the E is not referring to some actual thing called energy. It is referring to the kinetic energy of massless particles (photons).
Another way to think of it would be to look at an object, a pencil say, and describe it as having a length. Length is not a substance, but a measurement telling you how much of the Universe the pencil takes up. The actual thing going on is particles are bonded together to form the shape of a pencil. We can quantify how much pencil there is by talking about its length but we cannot treat "length" as a substance and release it from the pencil or somehow give it more. It can't be created or destroyed for instance. You chop the pencil in half and you still have the same amount of length, just distributed differently. It's the same with Energy.
Ability to make things happen is what Energy is and you can't create it out of nowhere (a Physicist's way of saying: things don't happen without a cause) and you can't destroy it (you can't have a cause without an effect). So always remember that although Energy is a useful tool for keeping track of things, it is not a substance and never an explanation. Even when you hear distinguished Scientists talking about it as if it's an actual thing, remember this is just shorthand vocabulary.
Energy = ability to make a change to the Universe.