Chemistry 1.6 Kinetics of Nuclear Decay and Nuclear Binding Energy
Half life sample questions
(1) Half life is two hours. What percent is left after 11.8hours? Not a perfect number of half lives so you can't give perfect answer but you can approximate it. -11.8 is close to 6 hours of decay. So answer would be between 5 half lives (10 hrs decay) and 6 half lives (12 hrs decay). - After 5 half lives 3.125% is left - After 6 half lives 1.5625% is left Answer should be closer to 1.5% so maybe about 1.6%. (2) You have 20g of a sample. 24 hours later you have 2.5g left. What is the half life? - How many times has the amount I have been cut in half? 20-10-5-2.5 Its been cut in half three times. 24/3= 8hrs is one half life.
Kinetics of Nuclear Decay
Kinetics of nuclear decay is always a first order process for the spontaneous routes of nuclear decay. This means: -the rate at which decay happens is proportional to how much you have. -also means you have a constant half life. Half life is time it takes for half of sample to decay. It doesn't matter how much you have, it takes same amount of time for half of sample to decay. This makes it convenient for approximating stuff in you head (involving eq in picture). Example: you have a radioactive isotope with a half-life of 10 years. You start with 100g of isotope. How much would you have left after ten years? - in ten years you have 50g - in another ten years you have 25g - in another ten years you 12.5g - in another ten years you have 6.25g..etc. You can have various units for half life such as percentages, fractions and activities. In fractions example, after four half lives you have 1/16th left. So how much has decayed? The rest (15/16ths) has decayed. In activities example: you can have different units for activity depending on how many radioactive decays are happening per second or something. -So if you have sample thats giving of 8 somethings per minute (thats how much radiation its giving off), how much radiation would it give off after undergoing a half life? It would give off 4 somethings per minute. Theres a lot of different units and ways to measure radioactivity (any of them would work here).
Nuclear Binding Energy continued.
Nuclear binding energy is the energy supplied by the strong nuclear force that holds the nucleus together. Where does this energy come from? . If you want to make a helium nucleus, you take two protons and two neutrons and put them together in a nucleus. - Each proton and neutron weighs one gram. You have total mass of 4 grams. Put them all together in a nucleus and you get Helium nucleus. -This helium nucleus should weigh 4 grams but it doesn't. It weighs around 3.999 grams. That missing mass is converted into energy and this is the energy that hold everything together in the nucleus (Nuclear Binding Energy). A nucleus always weighs a little less than all of its components/nucleons because its converted that mass into energy.
Fusion and Fission
The most stable nucleus on the planet is Iron-56 Fe(56) Every other nucleus is nucleus. - Lighter nuclei can combine with the lighter nuclei to come closer to weighing 56. This is FUSION (when lighter nuclei combine to form something larger) - Heavier nuclei would like to divide into multiple nuclei to be closer to weighing 56 as well. This is FISSION (when heavy nuclei separate into smaller nuclei) - In a nuclear reactor we typically do Fission. Thats why we use big elements. - Fusion typically happens in atomic bombs and at the center of a star. Lots of hydrogen and helium combining to form heavy nuclei.
Nuclear Binding Energy Iron 56 Most Stable Nucleus
What we mean when we say Fe-56 is the most stable nucleus is that is has the highest Nuclear Binding Energy per nucleon. Nucleon: anything that lives in the nucleus (proton or neutron) Babysitting analogy: Hire Cory to babysit and pay him $10/hour. Hire Christy to babysit and pay her $50/hour. Who got the better deal? It depends on how many kids you're watching. Cory would have had to watch 2 kids ($5 an hour per kid) and Christy would have had to watch 50 kids ($1 an hour per kid). Cory clearly got the better deal. Same thing in this situation. You have to see how many nucleons have to be held together in that nucleus.
Nuclear Binding Energy and E=(delta)mc^2 (calculating nuclear binding energy using mass defect)
You can figure out how much a nucleus should weigh and compare it to how much it actually weighs. You take the mass and plug it into E=(delta)mc^2. - energy: joules - delta m (Mass defect): means the difference in mass (how much nucleus should weigh - how much nucleus actually weighs). Aka the mass that was converted into energy. units (kg) - c: 3x10^8 meters/sec On exam they may just want you to do a comparison: In this situation instead of using equation you can just remember Fe-56. - example: who has a higher nuclear binding energy per nucleon? Chromium 54 or Uranium 238? Cr-54 has higher NBE per nucleon because it has a closer mass number to Fe-56, which is the most stable. So not only is Fe-56 the most stable, anyone close in mass number to him is more likely to be stable as well (not guaranteed but most likely). - So if you have some big calculation they're expecting you to do and you don't have time, you can see who is closer to Fe-56.