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.