# radioactivity (1)

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Radioactivity

RadiationRadiation: The process of emitting energy in the form of waves or particles. Where does radiation come from?Radiation is generally produced when particles interact or decay. A large contribution of the radiation on earth is from the sun (solar) or from radioactive isotopes of the elements (terrestrial). Radiation is going through you at this very moment!http://www.atral.com/U238.html

IsotopesWhats an isotope?Two or more varieties of an element having the same number of protons but different number of neutrons. Certain isotopes are unstable and decay to lighter isotopes or elements. Deuterium and tritium are isotopes of hydrogen. In addition to the 1 proton, they have 1 and 2 additional neutrons in the nucleus respectively*.Another prime example is Uranium 238, or just 238U.

RadioactivityBy the end of the 1800s, it was known that certain isotopes emit penetrating rays. Three types of radiation were known: Alpha particles (a) Beta particles (b) Gamma-rays (g)

Where do these particles come from ?These particles generally come from the nuclei of atomic isotopes which are not stable. The decay chain of Uranium produces all three of these forms of radiation. Lets look at them in more detail

Alpha Particles (a)Radium R22688 protons138 neutronsRadon Rn222Note: This is the atomic weight, which is the number of protons plus neutrons86 protons136 neutrons+nnppa (4He)2 protons2 neutronsThe alpha-particle (a) is a Helium nucleus. Its the same as the element Helium, with the electrons stripped off !

Beta Particles (b)CarbonC146 protons8 neutronsNitrogenN147 protons7 neutrons+e-electron(beta-particle)We see that one of the neutrons from the C14 nucleus converted into a proton, and an electron was ejected. The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred:

n p + e ( + n )Yes, the same neutrino we saw previously

Gamma particles (g)In much the same way that electrons in atoms can be in an excited state, so can a nucleus.NeonNe2010 protons10 neutrons (in excited state)10 protons10 neutrons (lowest energy state)+gammaNeonNe20A gamma is a high energy light particle. It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.

Gamma RaysNeonNe20+The gamma from nuclear decay is in the X-ray/ Gamma ray part of the EM spectrum (very energetic!)NeonNe20

How do these particles differ ?* m = E / c2

ParticleMass* (MeV/c2)ChargeGamma (g)00Beta (b)~0.5-1Alpha (a)~3752+2

Rate of DecayBeyond knowing the types of particles which are emitted when an isotope decays, we also are interested in how frequently one of the atoms emits this radiation. A very important point here is that we cannot predict when a particular entity will decay. We do know though, that if we had a large sample of a radioactive substance, some number will decay after a given amount of time. Some radioactive substances have a very high rate of decay, while others have a very low decay rate. To differentiate different radioactive substances, we look to quantify this idea of decay rate

Half-Life The half-life (h) is the time it takes for half the atoms of a radioactive substance to decay.

For example, suppose we had 20,000 atoms of a radioactive substance. If the half-life is 1 hour, how many atoms of that substance would be left after:10,000 (50%) 5,000 (25%) 2,500 (12.5%)1 hour (one lifetime) ?2 hours (two lifetimes) ?3 hours (three lifetimes) ?

Lifetime (t) The lifetime of a particle is an alternate definition of the rate of decay, one which we prefer. It is just another way of expressing how fast the substance decays.. It is simply: 1.44 x h, and one often associates the letter t to it. The lifetime of a free neutron is 14.7 minutes {t (neutron)=14.7 min.} Lets use this a bit to become comfortable with it

Lifetime (I) The lifetime of a free neutron is 14.7 minutes. If I had 1000 free neutrons in a box, after 14.7 minutes some number of them will have decayed. The number remaining after some time is given by the radioactive decay lawN0 = starting number of particles t = particles lifetimeThis is the exponential. Its value is 2.718, and is a very useful number. Can you find it on your calculator?

Lifetime (II)Note by slight rearrangement of this formula:Fraction of particles which did not decay: N / N0 = e-t/tAfter 4-5 lifetimes, almost all of theunstable particles have decayed away!

# lifetimesTime(min)Fraction of remaining neutrons0t01.01t14.70.3682t29.40.1353t44.10.0504t58.80.0185t73.50.007

Chart1

1

0.3678794412

0.1353352832

0.0497870684

0.0183156389

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0.0024787522

0.000911882

0.0003354626

0.0001234098

Lifetimes

Fraction Survived

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001.0000

114.70.3679

229.40.1353

344.10.0498

458.80.0183

573.50.0067

688.20.0025

7102.90.0009

8117.60.0003

9132.30.0001

Sheet1

0

0

0

0

0

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0

0

0

0

Lifetimes

Fraction Survived

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Lifetime (III) Not all particles have the same lifetime. Uranium-238 has a lifetime of about 6 billion (6x109) years ! Some subatomic particles have lifetimes that are less than 1x10-12 sec ! Given a batch of unstable particles, we cannot say which one will decay. The process of decay is statistical. That is, we can only talk about either, 1) the lifetime of a radioactive substance*, or 2) the probability that a given particle will decay.

Lifetime (IV) Given a batch of 1 species of particles, some will decay within 1 lifetime (1t), some within 2t, some within 3t, and so on We CANNOT say Particle 44 will decay at t =22 min. You just cant ! All we can say is that: After 1 lifetime, there will be (37%) remaining After 2 lifetimes, there will be (14%) remaining After 3 lifetimes, there will be (5%) remaining After 4 lifetimes, there will be (2%) remaining, etc

Lifetime (V)

If the particles lifetime is very short, the particles decay away very quickly. When we get to subatomic particles, the lifetimes are typically only a small fraction of a second! If the lifetime is long (like 238U) it will hang around for a very long time!

Lifetime (IV)What if we only have 1 particle before us? What can we say about it? Survival Probability = N / N0 = e-t/t

Decay Probability = 1.0 (Survival Probability)

# lifetimesSurvival Probability (percent)Decay Probability = 1.0 Survival Probability (Percent)137%63%214%86%35%95%42%98%50.7%99.3%

Summary Certain particles are radioactive and undergo decay. Radiation in nuclear decay consists of a, b, and g particles The rate of decay is give by the radioactive decay law: Survival Probability = (N/N0)e-t/t After 5 lifetimes more than 99% of the initial particles have decayed away. Some elements have lifetimes ~billions of years. Subatomic particles usually have lifetimes which are fractions of a second Well come back to this!

To be more clear, deuterium contains 1 proton and 1 neutron in the nucleus, and tritium contains 1 proton and 2 neutrons in its nucleus. Both isotopes behave similarly to ordinary hydrogen, as this chemical behavior is mostly driven by the atomic electrons.Note: The 226 refers to the atomic weight, which is the equal to the number of protons plus neutrons

Note that in beta decay, the atomic mass not change, since the neutron and proton have nearly the same mass

So, lifetime is just another measure of how quickly the particles will decay away.

If the lifetime is short, the particles will decay away quickly.

If the lifetime is long (like some U-238 isotopes), it will be around for a very long time!

* In the context of talking about the lifetime, we are implying that we have a large sample of the substance containing many radioactive atoms. The lifetime represents the fraction pf atoms which will have decayed. Unfortunately, we cannot say exactly which ones will have decayedNote: The number e is very common in math and physics. It has the value: e = 2.718But, what if we only have 1 particle before us? What can be said about its decay?

In this case, the radioactive decay law gives the probability that this particle will have NOT decayed (I.e., it survived without decaying) after some time. Survival Probability = N / N0 = e-t/t

So, the probability that a single unstable particle will survive after 1 lifetime is 37%;5% chance itll be around after 2 lifetimes; 2% chance itll be around after 3 lifetimes, and so on Now, sometimes, we want to know the probability for a certain particle to decay. This is simply obtained by saying:Decay Probability = 1.0 (Survival Probability)

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