(has to do with the nucleus, get it?!) Take Home Unit Packet! (you’ll get this joke better once you read the next page….) I) Intro In 1896 French chemist Antoine Becquerel accidentally discovered that uranium emits invisible rays. Marie and Pierre Curie were his students and they showed that film could be “fogged” or exposed by the rays given off by uranium ore. This radiation was a result of…. II) Radioactive Decay (Radioactivity) A) What is it? The spontaneous breakdown of an atom’s nucleus. In a chemical reaction the nucleus never changes, only electrons are transferred or shared. In a nuclear reaction the nucleus always changes, thus changing the identity of the atom. B) Why does it occur? The nucleus may be unstable based on the neutron-to-proton ratio. It will then spontaneously break down until it attains a more stable neutron-to-proton ratio. Check out the graph on the following page which shows the number of neutrons in the atom as it relates to the number of protons in an atom. The belt of stability represents a neutron-to-proton ratio which is stable, resulting in nuclei that do NOT decay. Anything outside of the belt of stability has a neutron-to-proton ration which is unstable, resulting in nuclei that do decay. C) What does it result in? The decay process results in the release of energy (radiation) and particles. A new element is also formed as the nucleus breaks down and changes its composition. Because the nucleus changes, the identity of the element also changes. This is why a new element can be formed in a nuclear reaction, but not a chemical reaction. D) Which elements are naturally radioactive? Technetium (atomic number= 43), Polonium (atomic number= 84) and any element higher are always radioactive. Sometimes an element which is normally stable has a certain isotope that is radioactive called a radioisotope. Many times these radioisotopes are high neutron isotopes (ex. C-12 is not radioactive, C-14 is radioactive). Most elements are NOT radioactive and do NOT decay. Still, many elements do have a rare isotope that is radioactive. Elements 84 and above are always radioactive, no matter what the isotope is. E) What is natural transmutation? The spontaneous changing from one element to another. This is really is the same thing as radioactive decay but with a new focus. Natural means that it happens in nature without any outside intervention. The word transmutation specifically describes the formation of a new element. This is exactly what happens during radioactive decay, the formation of a new element. F) What factors do NOT affect radioactive decay? Unlike chemical reactions, temperature, pressure, concentration, surface area, and catalysts do NOT affect the decay rate. The decay is determined only by the stability of the specific nucleus and is thus not affected by outside forces. Therein lies one of the problems of radioactivity, it can’t be speeded up or slowed down! It does what it does and there’s nothing you can do about it! Number of Neutrons vs. Number of Protons in an Atom Radioactive Decay Worksheet 1. Define radioactivity. 2. How are chemical and nuclear reactions different from one another? 3. Why do nuclei spontaneously decay? 4. What is the belt of stability? 5. An element has 50 protons and 90 neutrons. Will the nucleus breakdown? Why or why not? 6. Will a nucleus of Zn-65 be stable or unstable? Explain. (Hint: the 65 represents the mass number of zinc) 7. What are the products of radioactive decay? 8. List elements which are always radioactive. 9. What is a radioisotope? 10. Define natural transmutation. 11. How would an increase in temperature affect the rate of radioactive decay? III) Types of Radioactive Decay Please note Table O as you read about each decay mode. Note: protons and neutrons are of interest in this unit, but they are NOT types of radioactive decay. A) Alpha Decay () An alpha particle is released from the nucleus as it decays. An alpha particle is the same thing as a helium nucleus and is often given the notation He. Alpha particles have a mass of 4 (the top number) and a charge of +2 (the bottom number). Alpha particles are very large and move very slowly. They are not considered to be dangerous when they are emitted from an atom’s nucleus because they cannot pass through even a piece of paper let alone a person’s skin. We say that alpha particles have a low penetrating power. It can, however, cause matter around it to ionize, so it is considered to have a high ionizing ability. B) Beta Decay (-) A beta particle is released from the nucleus as it decays. A beta particle is the same thing as an electron and is often given the notation -1e. A beta particle has a mass of 0 (the top number) and a charge of –1 (the bottom number). You may wonder how an electron can be emitted from an atom’s nucleus. In fact, a neutron breaks down into an extra proton which remains in the nucleus and an electron which is given off. Beta particles are of medium size and move at a medium speed. Beta particles are slightly more dangerous than alpha particles, but they can be stopped by something thicker than paper such as metal foil. We say that beta particles have a medium penetrating power. It can cause matter around it to ionize, so it is considered to have a medium ionizing ability. C) Gamma Radiation () Unlike alpha and beta particles, gamma radiation is not a particle released from the nucleus as it decays. Instead, it is a form of electromagnetic radiation. It has a mass of 0 (the top number) and a charge of 0 (the bottom number). Almost all radioactive decay modes are accompanied by the release of gamma radiation. Gamma radiation moves at the speed of light, so it is very fast. Gamma radiation is very dangerous, since it can only be stopped by lead or concrete. We say that gamma radiation has a very high penetrating power. This is the cause of radiation sickness associated with radioactive waste spills or atomic bomb fall out. It does not cause matter around it to ionize, so it has almost no ionizing ability. Highly recommended: check out the following web link for a nice review with good visuals. Try out the practice quiz for extra practice. http://www.darvill.clara.net/nucrad/types.htm Note: the last form of decay is still very important, it’s just that most textbooks and websites don’t list it under the 3 main types of decay. Oh well, we’ll still learn about it! D) Positron Decay (+) A positron particle is released from the nucleus as it decays. A positron particle is the same thing as a positively charged electron and is often given the notation +1e. A positron has a mass of 0 (the top number) and a charge of +1 (the bottom number). You may wonder how a positively-charge electron is produced. In fact, a proton breaks down into an extra neutron which remains in the nucleus and positron which is given off. Decay Mode Worksheet 1. List the four types of radioactive decay. 2. Use Table O to write the correct notation for an alpha particle. Describe what each number in the notation means. 3. Why is the emission of an alpha particle not particularly dangerous to people? 4. How is a beta particle produced by a nucleus? 5. Describe the speed and penetrating power of a beta particle. 6. What can stop a beta particle from passing? 7. How is gamma radiation different from the other forms of decay? 8. Why is gamma radiation so dangerous to people? 9. What is a positron? How is it produced? 10. What subatomic particle listed on Table O has the same charge as gamma radiation? 11. Name all subatomic particles listed on Table O that would be affected by a magnet. IV) Radioactive Decay Equations A radioactive decay equation should always have one reactant (the element decaying), a particle emitted as a product (based on the decay mode) and the new element created as a product. The new element is determined by making sure the masses (top number) on both sides of the equation are equal and the charges (bottom number) on both sides of the equation are equal. The bottom number is also the atomic number and ultimately determines the identity of the new element. Given a radioisotope, you can look on Table N to find out its decay mode. We will discuss half-life later in this unit. Rules for Equation Writing 1. You will be given a radioisotope (also known as a nuclide). Since it decays on its own, write it down as the only reactant. You may have to determine the atomic number off of the Periodic Table. Add an arrow. 2. Using Table N, determine the decay mode. 3. Using Table O, determine the full notation of the emitted decay particle from Table N. 4. Write this notation for the particle to the right of the arrow as a product. 5. The top numbers (mass) on each side of the equation must be equal on both sides. Determine the top number of the new element. 6. The bottom numbers (nuclear charge) must be equal on both sides. Determine the bottom number of the new element. 7. Using the lower number (atomic number) and your Periodic Table, write the symbol of the new element. Examples: Read through the examples step by step so that you fully understand how to write radioactive decay equations. Writing Decay Equations Worksheet 1. Compare the decay modes of K-37 and K-42, according to Table N. 2. Write the decay equation for K-37. 3. Write the decay equation for K-42. 4. Which of the following would be more dangerous, radon-222 or cobalt-60 in the same dosage? Explain. 5. Write the decay equation for radon-222. 6. Write the decay equation for cobalt-60. V) Half-life A) What is it? The amount of time it takes for half of a sample’s nuclei to decay. The amount of time for half of the sample to decay, regardless of amount, remains CONSTANT. It is important that you realize that half of the nucleus doesn’t decay, but half of the atoms in a given sample decay during after one half-life. B) Who cares? What’s interesting about half-life is that no matter how many atoms you start with, half of them will decay after one half-life. After a second half-life, half of the atoms that remain after the first decay, decay themselves. After a third half-life half of the atoms that remain after the second decay, decay themselves and so on. Note: the time that passes after each half-life does NOT change! (see the graph below) Although from a mathematical standpoint you wouldn’t expect to ever reach zero where all atoms are decayed, in reality, eventually all atoms will decay and you WILL reach zero. C) How do I know what a radioisotopes’ half-life is? Use Table N to look up the half-life for each nuclide. Each radioisotope has its own distinct half-life that cannot be changed. Changes in temperature, pressure, concentration, surface area, and catalysts do NOT affect the decay rate and thus do NOT affect the halflife. D) What does the value for half-life tell me? Each radioisotope has its own distinct half-life value which tells you how long it takes for half of the sample to decay. Radioisotopes with short half-lives are less dangerous because they decay more quickly. Radioisotopes with long half-lives are more dangerous because they decay slowly and thus, stay radioactive longer. This is a particular problem with radioactive waste. Highly recommended: check out the following web link for a nice review with good visuals. Try out the practice quiz for extra practice. http://www.darvill.clara.net/nucrad/hlife.htm Half-life Concepts Worksheet 1. What is half-life? 2. After three half-lives, what fraction of the original sample would remain? Explain. 3. A 50 gram sample of a radioisotope undergoes 2 half-lives. How many grams would remain at the end? Explain. 4. Name the element on Table N that has the shortest half-life that undergoes alpha decay. 5. Would the nuclide from #3 be dangerous to living things based on its halflife? Why or why not? 6. Which radioisotope on Table N has the longest half-life? 7. Would the nuclide from #5 be dangerous to living things based on its halflife? Why or why not? 8. A radioactive sample of C-14 is heated. How is the half-life affected? VI) Half-life Calculations Check out the following example problems shown below. Use them as models for the worksheet that follows. Ex 1) How many grams remain of a 10.0 gram sample of cobalt-60 after 15.78 years? Step 1: Determine the half-life from Table N: 5.26 years Step 2: Calculate the number of half-lives that have passed: # of half-lives = total time/1 half-life = 15.78 y/5.26 y = 3 half-lives Step 3: Set up a chart that shows the amount decaying by ½ with the passing of each half-life. Hint: Make sure that the initial amount is always before the first half-life at 0. # of half-lives 0 1 2 3 Fraction remaining 1 1/2 1/4 1/8 Grams remaining 10.0 g 5.00 g 2.50 g 1.25 g Step 4: State the final answer: After 15.78 years (3 half-lives), 1.25 grams of cobalt-60 remain. Ex 2) What mass of iodine-131 remains 32 days after a 100. g sample of the isotope is obtained. Step 1: Determine the half-life from Table N: 8.07 days Step 2: Calculate the number of half-lives that have passed: # of half-lives = total time/1 half-life = 32 d/8.07 d = 4 half-lives Step 3: Set up a chart that shows the amount decaying by ½ with the passing of each half-life. Hint: Make sure that the initial amount is always before the first half-life at 0. # of half-lives 0 1 2 3 4 Fraction remaining 1 1/2 1/4 1/8 1/16 Grams remaining 100. g 50.0 g 25.0 g 12.5 g 6.25 g Step 4: State the final answer: After 32 days (4 half-lives), 6.25 grams of iodine-131 remain. Ex 3) A sample of an isotope decays from 100. grams to 25.0 grams in 20 days. What is the half-life of the unknown radioisotope? Step 1: Determine the number of half-lives with a chart showing the decay of the original amount to the final amount: # of half-lives 0 1 2 Fraction remaining 1 1/2 1/4 Grams remaining 100. g 50.0 g 25.0 g Thus, 2 half-lives have occurred. Step 2: Divide the total time by the number of half-lives to obtain the half-life: half-life = total time/# of half-lives = 20 d/2 half-lives = 10 days Step 3: State the final answer: The half-life (time for half to decay) is 10 days. Ex 4) If a sample of Sr-90 has a mass of 100. grams, how long will it take to decay such that only 12.5 grams of Sr-90 remains? Step 1: Determine the half-life from Table N: 28.1 years Step 2: Determine the number of half-lives with a chart showing the decay of the original amount to the final amount: # of half-lives 0 1 2 3 Fraction remaining 1 1/2 1/4 1/8 Grams remaining 100. g 50.0 g 25.0 g 12.5 g Thus, 3 half-lives have occurred. Step 3: Determine the total time by multiplying the half-life by the number of half-lives: 28.1 y x 3 = 84.3 y State 4: State the final answer: It takes 84.3 years for Sr-90 to decay from 100. grams to 12.5 grams. Half-life Calculations 1. How much of a 100. gram sample of 198Au is left after 8.10 days? 2. A 50.0 gram sample decays to 12.5 grams in 14.4 seconds. What is its halflife? 3. How much of a 750.00 gram sample of K-42 is left after 62.00 hours? 4. What is the half-life of an element if a 500. gram sample decays to 62.5 grams in 639,000 years? 5. If there are 25.0 grams of a sample of thorium-232 left after 2.80 x 1010 years, how many grams were in the original sample? 6. How long will it take for 16 grams of Ra-226 to break down until only 1.0 grams remain?
