3. (20 pts) Go to the website: https://www.nndc.bul.govudat2/ Click on "decay mode" on the top bar (to the right of "half-life"). Find Plutonium-244 (244Pu) by mousing over the chart near the upper right. Click on any Pu box you find and then zoom in using the slider and look more closely. (a) Take a picture of the zoomed table of nuclides with 244Pu in the center and submit it with your homework to show that you did the problem using this chart. No credit without the picture. (b) Using the color coding (yellow is alpha-decay, pink is beta-decay), figure out the first 3 steps in its decay chain: 244z Pu >> AzX + ?> AZY +?> AzW + ? Fill in all the A, Z (different for each) and the X, Y, W for the elements and the "?" for the radiation. (c) The half-life of 244Pu is 80 million years, but what are the half-lives for X and Y? (d) If you had 100 atoms of X, how long will you have to wait until you have 25 atoms of W? We talk this way to make it easy, but it is the same as asking "Once you have an atom of X, when do you have a 25% chance of seeing an atom of W appear?" You don't need any formula to do this, just the definition of a half-life.4. (20 pts) This problem is similar to the problem in class where you stand next to a gram of radium. Go to Lecture 28 (April 8 in Tophat). The units are on slide 3 and the similar problem is on slides 7-10. Suppose you throw away your smoke detector in the garbage and a racoon eats the internal radioactive source, will the racoon die? Start by nding out the dose received by the racoon. In other words, how many J/kg (Gy) does it receive over those 24 hours while the radioactivity is in its body? Then adjust to Sieverts using Q (see below). This is ultimately a simple units problem. Convert activity in nCi to Bq (decays per second) and then each decay has the energy of one alpha (6.05 MeV better convert that to J). Think it through there is no \"formula\". The radioactive isotope in your smoke detector is Americium-24l. Type of decay = alpha-decay -) Q = 20 Energy of alpha = 6.05 MeV Activity = 62 nCi Weight of racoon = 6 kg Time it takes to pass through its system = 24 hours Once you know the dose, you can compare to the following table to determine if the dose is enough to kill the racoon or not. Even though the table says \"human body\5. (15 pts) In a nuclear reactor, neutrons destabilize 235U and many different reactions occur. Here is just one way that Uranium can ssion: n + 2330' -) \"21.51 + 381' + n + Q where Q just represents the energy released. (a) Fill in the '? and write down the full reaction equation. You need to look up Z to match to the element name using a periodic table. There are several examples in slides 4-11 of Lecture 27B on Tophat, including a periodic table. (b) Find the energy released by one such reaction. Give the answer in units of Joules. Use the following masses for the isotopes in question: m (U) = 2350439 u m(La) = 147.9320 u m(Br) = 86.9207 u (c) How many atoms are in a gram of U-235? (d) What is the energy (in Joules) released by ssioning a gram of U-235 through this reaction