Radioactivity

Radiation Radiation: 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

Isotopes What’s 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. 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.

Radioactivity By 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. Let’s look at them in more detail…

Note: This is the atomic weight, which is the number of protons plus neutrons Alpha Particles (a) Radium R226 Radon Rn222 + p n n p a (4He) 88 protons 138 neutrons 86 protons 136 neutrons 2 protons 2 neutrons Note: The 226 refers to the atomic weight, which is the equal to the number of protons plus neutrons The alpha-particle (a) is a Helium nucleus. It’s the same as the element Helium, with the electrons stripped off !

Yes, the same neutrino we saw previously Beta Particles (b) Carbon C14 Nitrogen N14 + e- 6 protons 8 neutrons 7 protons 7 neutrons 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 ) Note that in beta decay, the atomic mass not change, since the neutron and proton have nearly the same mass… 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. Neon Ne20 Neon Ne20 + 10 protons 10 neutrons (in excited state) 10 protons 10 neutrons (lowest energy state) gamma A 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 Rays Neon Ne20 Neon Ne20 + The gamma from nuclear decay is in the X-ray/ Gamma ray part of the EM spectrum (very energetic!)

How do these particles differ ? Mass* (MeV/c2) Charge Gamma (g) Beta (b) ~0.5 -1 Alpha (a) ~3752 +2 * m = E / c2

Rate of Decay Beyond 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: Time #atoms remaining % of atoms remaining 1 hour (one lifetime) ? 10,000 (50%) 2 hours (two lifetimes) ? 5,000 (25%) 3 hours (three lifetimes) ? 2,500 (12.5%)

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.} Let’s 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 law N0 = starting number of particles t = particle’s lifetime This is the “exponential”. It’s value is 2.718, and is a very useful number. Can you find it on your calculator?

Fraction of remaining neutrons Lifetime (II) Note by slight rearrangement of this formula: Fraction of particles which did not decay: N / N0 = e-t/t # lifetimes Time (min) Fraction of remaining neutrons 0t 1.0 1t 14.7 0.368 2t 29.4 0.135 3t 44.1 0.050 4t 58.8 0.018 5t 73.5 0.007 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! After 4-5 lifetimes, almost all of the unstable particles have decayed away!

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. * 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 decayed…

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 can’t ! 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 Note: The number “e” is very common in math and physics. It has the value: e = 2.718

Lifetime (V) If the particle’s 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!

Decay Probability = 1.0 – Survival Probability (Percent) 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) # lifetimes Survival Probability (percent) Decay Probability = 1.0 – Survival Probability (Percent) 1 37% 63% 2 14% 86% 3 5% 95% 4 2% 98% 5 0.7% 99.3% But, what if we only have 1 particle before us? What can be said about it’s 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 it’ll be around after 2 lifetimes; 2% chance it’ll 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)

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… We’ll come back to this!