3.0 x 10 (4) Use the Schwarzchild formnila 20M where R. - Radius of a star, in meters, that would cause it to become a black hole Al = Mass of the star, in kilograms G - 6.7 x 10 11 m kg s2 , the gravitational constant c = 3 x 10" m/s, the speed of light to determine to what length the radius of the sun must be reduced for it to become a black hole. The mass of the sun is approximately 2 x 1090 kg. Exponents application #3: radioactive decay Plutonium-239 is the material we use in our nuclear things - weapons, submarines, etc. Plutonium-239 experiences radioactive decay, and has a half-life of 24,110 years. "Half-life" means that, if you begin with 100 kilograms of Plutonium-239: In 24,110 years, you'd still have 50 kilograms left... In another 24,110 years, you'd still have 25 kilograms left... etc. A half-life is the amount of time it takes for half of your material (in this case, Plutonium-239) to disappear. Note that, this stuff just won't go away! Things that experience radioactive decay don't completely disappear, they just... decay. This is why it is such a big concern when a nuclear submarine sinks: eventually, the salt water will eat through the steel and release the Plutonium (which, since it's decaying radioactively, will still exist). We can use the radioactive decay formula to describe how material decays: A = Aox where A= Mass of material, in kilograms, left at time t. Ao = Mass of the material, in kilograms, at the start of the decay t = time that has elapsed, in years A = the half-life of the material, in years. (5) Suppose you started with 100 kg of Plutonium-239. How many kg will be left after 10,000 years? (6) Suppose you started with 100 kg of Plutonium-239. How many years will it take for your supply to decay down to 10kg? (7) Carbon-14 is another element that experiences radioactive decay, with a half-life of 5,730 years. Carbon-14 is often found in living things (animals and plants), and begins to decay as soon as those things die. Because of this, scientists that find animal remains can often use Carbon-14 to estimate how long ago the animal or plant died. The C-14 content of an ancient piece of wood was found to have three tenths of that in living trees (indicating 70% of the C-14 had decayed). How old is that piece of wood