RADIOACTIVE DECAY & HALF-LIFE CALCULATIONPresenters: Damion Lawrence and Michael Ward

PREREQUISITE KNOWLEDGE For mastery of the content presented in this presentation, students should have been taught:Atomic Structure Mass numberAtomic numberThe difference between a parent atom and a daughter atomthe nature of the three types of radioactive emissionsAnalyzing a graph

PRESENTATION OBJECTIVES At the end of this presentation, students will be able to:State what is meant be the term Radioactive decayDefine the term half-lifeinterpret nuclear reactions in the standard formsolve problems involving half-lifeExplain how Carbon Dating is accomplished

RADIOACTIVE DECAY(section E: Specific objective 3.2) This is the process by which a nucleus of an unstable atom (i.e. Radioisotope) releases energy and particles ( i.e. Alpha particle, beta particle, gamma ray.) to become a more stable atom.

ALPHA DECAY

Two protons and two neutrons are lost from a nucleus when it emits an alpha particle. This means that:The mass number decreases by 4The atomic number decreases by 2

BETA DECAY

In beta decay, a neutron changes into a proton plus an electron. The proton stays in the nucleus. The electron leaves the atom with high energy as a beta particle.The nucleus has one more proton and one less neutron when it emits a beta particle. This means that:The mass number stays the sameThe atomic number increases by 1

GAMMA DECAY In gamma decay, a nucleus changes from a higher energy state to a lower energy state through the emission of electromagnetic radiation (photons). The number of protons (and neutrons) in the nucleus does not change in this process, so the parent and daughter atoms are the same chemical element.

TRANSMUTATIONTransmutation is the changing of one element into another by radioactive decay, nuclear bombardment, or similar processes. In other words, it is the Transformation of one element into another by one or a series of nuclear reactions.

TRANSMUTATION When an unstable atom undergoes an Alpha or Beta decay, it changes into a new element. This process is known as Transmutation. This can be further examined by a Nuclear Equation . Since each element in the periodic table has a unique atomic number and this number changes when it undergoes an Alpha decay or beta decay, it can be argued that transmutation will occur during both decays.

TRANSMUTATIONIn the gamma decay as no particles either protons or nucleons are released so the element before the radioactive gamma decay and after the gamma decay remains same. In other words, the number of protons (and neutrons) in the nucleus does not change in this process, so the parent and daughter atoms are the same chemical element.

HALF-LIFE (T1/2)

(section E: Specific objective 3.10)This is the amount of time required for half the amount of a radioactive substance to decay. The half life of any given radioactive isotope does not vary with temperature ,pressure or any other condition. Nothing can speed up or slow down the rate at which a given isotope decays.

HALF-LIFE (T1/2)The half-life of some isotope is a fraction of a second while others can be up to billions of years.. For example uranium-238 has a half-life of 4.5x 109 years , while oxygen-19 has a half life of 29.4 seconds

HALF-LIFE (T1/2)consider what would happen to a 100g sample of lead which has a half-life of 22 years. At the end of the 22 years only 50g would be lead-210. At the end of another 22 years 25g would be remaining. This process will continue until extremely small amounts of lead-210 remains.

THE HALF-LIFE EQUATION.

Where A0 = Original amount of radioactive substance An = amount of radioactive substance remaining after n half-lives n= number of half-lives

TIME ELAPSE EQUATION

Time Elapse(T) = number of half-lives (n) x half-life (T1/2)

Example 3A radioactive isotope of xenon, xenon-125, has a half-life of 17 hours. If we start with 0.2500g, how many milligrams will remain after 2 days and 3 hours?

Solution to Example 3Add 17 hours (half-life) each time Time (h)Amount(g)Divide the amount remaining by 2 each time00.2500170.1250340.0625510.03125

Therefore 0.03125g or 31.25mg will remain after 2days and3hours (51 hours)

Alternative Solution to example 3GivenT1/2 = 17 hrs.Time elapse = 2days 3hrs ( or 51 hrs)Ao = 0.2500gAn =?

Alternative Solution to example 3 (contd)Step 1 (find number of Half-lives)From Time Elapse = number of half-lives (n) x half-lives (T1/2)number of half-lives = Times Elapse/ half-lifeTherefore , n = 51hrs/17hrs = 3Step 2 (find An)From 2n = Ao/An , An = Ao/2n An = 0.2500g / 23 , An = 0.2500g/8 , An = 0.03125g or 31.25mg (answer)

Example 4Strontium-90(2.500g) was in a 1960 atomic explosion at Johnson Island at the pacific test site. The half life of Strontium-90 is 28 years in what year will only 0.3125g remain?

Solution to Example 4Divide the amount remaining by 2 each timeAmounts (g) Time and yearAdd 28 years(half-life ) each time.2.5000(1960)1.25028(1988)0.62556(2016)0.31284(2044)

Alternative Solution to example 4GivenT1/2 = 28 yearsAo = 2.500gAn = 0.3125g

Alternative Solution to example 4 (contd)Step 1 ( find the # of Half-lives (n) )From 2n = Ao/An 2n = 2.500g/0.3125g 2n = 8 Therefore n = 3Step 2 (find time elapse)Time Elapse = n x T1/2 , Time Elapse = 3 x 28 years, , Time Elapse = 84yrsStep 3 ( add elapse time to initial date )The year in which 0.3125g remains= 1960 +84 = 2044 (answer)

CARBON DATING

(section E: Specific objective 3.11)A radiometric dating method for determining the age of life forms which have died in the relatively recent past, having a limit of accuracy of about 60,000 years. Carbon dating is the result of cosmic radiation which bombards the Earths atmosphere, which constantly produces more 14C isotopes from 14N.

CARBON DATINGFor radiocarbon dating to be possible, the material must once have been part of a living organism. This means that things like stone, metal and pottery cannot usually be directly dated by this means unless there is some organic material embedded or left as a residue.

Activity 1A radioactive source is found to be emitting, on average, 880 particles per second. If the source has a half life of 25 minutes, how much time will elapse before the average emission rate becomes 110 per second?

( Source: CSEC Physics Paper-03 , May 2007)

Activity 2How many half-lives would it take for a sample of Carbon-14 to be reduced to 1/32 of its original mass?

Given that Carbon -14 has a half-life of 5700 years, determine how long it would take for this reduction to occur.

(Source: CSEC Physics Paper -02 May 2008)

Activity 3A gram of living plant material with carbon-14, decays at a rate of about 16 disintegrations per minute. When the plant dies, the carbon-14 decays, with a half-life of 5600 years. A gram of the dead plant is found to decay at about 1 disintegration per minute. Calculate the probable age of the plant.

(Source: CSEC Physics Paper -02 May 2011)

GLOSSARY OF TERMS Atomic number (or Proton number): The number of proton in the nucleus of an atom. The atomic number determines which element an atom is.

GLOSSARY OF TERMS Daughter atom : A daughter atom refers to the isotope that is the product atom formed during the radioactive decay in a nuclear reaction.

GLOSSARY OF TERMS Emission: the act of sending out gas, heat, light, etc

GLOSSARY OF TERMS Isotope : Any atom having the same atomic number but different mass number. In other words, they have the same number of protons and electrons but different number of neutrons.

GLOSSARY OF TERMS Mass number (or Nucleon number): The mass number (A), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus.

GLOSSARY OF TERMS Nuclei : plural of nucleus ( i.e. the central part of an atom that comprises nearly all of the atomic mass and that consists of protons and neutrons)

GLOSSARY OF TERMS Parent Atom: A parent atom is a term used to describe the original state of an atom or element before it undergoes a chemical change.

GLOSSARY OF TERMS Radioisotope: radioactive form of an element, consisting of atoms with unstable nuclei, which undergo radioactive decay to stable forms, emitting characteristic alpha, beta, or gamma radiation.

GLOSSARY OF TERMS Radiometric dating: Radiometric dating is a technique used to estimate the age of rocks and other objects based on the fixed decay rate of radioactive isotopes

REFERENCES Caribbean Examinations Council (CXC) ,2014 . Physics CSEC Past PapersHow Carbon Dating Works. Retrieved from: https://www.youtube.com/watch?v=Kcuz1JiMk9k How Does Radiocarbon Dating Work? - Instant Egghead #28. Retrieved from: https://www.youtube.com/watch?v=phZeE7Att_s Radioactive Decay & Nuclear Equations. Retrieved from: https://www.youtube.com/watch?v=uF6EgMQ8STA Solving half life problems. Retrieved from: https://www.youtube.com/watch?v=_pcPz1VXVms

REFERENCESNuclear Physics 8.1: Natural Transmutations. Retrieved from: https://www.youtube.com/watch?v=I7WTQD2xYtQ What are Alpha, Beta and Gamma Decay? Retrieved from: https://www.youtube.com/watch?v=4FuvyIDM_eQ What does the term half-life mean? Retrieved from: https://www.youtube.com/watch?v=tzM6aK5QbSU

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