# chapter 6: isotopes. radioactivity: the spontaneous breakdown of a nucleus. radioactive isotopes:...

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- Slide 1
- Chapter 6: Isotopes
- Slide 2
- Radioactivity: the spontaneous breakdown of a nucleus. Radioactive Isotopes: atoms that undergo spontaneous breakdown of their nuclei to form other isotopes. Alpha ( ) emission: the release of 2 protons and 2 neutrons (the equivalent of a He nucleus). Beta ( - ) particle emission: the breakdown of a neutron to yield a proton and an electron; the electron is released and the new proton stays. This results in a new element with the same atomic weight as the parent element. Positron ( + ) particle emission: there is a breakdown of a proton to form a neutron and a positron. The positron is released creating a new element with the same atomic weight as the parent element. K-electron capture ( ): An electron is captured by a nucleus, merged with a proton and forms a new neutron. The result is a new element with the same atomic weight as the parent element.
- Slide 3
- Alpha Particle Emission
- Slide 4
- - decay + decay
- Slide 5
- K-electron Capture
- Slide 6
- Slide 7
- Radioactive Decay and Growth The decay of a radioactive isotope is a first-order reaction and can be written: dN/dt =- N Where N is the number of unchanged atoms at the time t and is the radioactive decay constant. This equation can be rewritten as: N = N o e - t Where N o is the number of atoms present at t = 0. This is the basic form of the radioactive decay equation.
- Slide 8
- Half-life: the length of time that it takes for half of the atoms to spontaneously decay. t = ln2 / = 0.693 / The radioactive decay equation can also be written in terms of activity. A = A o e - t Where A is the activity at some time t, and A o is the activity at t = 0. Rearranging this equation and solving for t yields: t = 1/ ln (A o /A)
- Slide 9
- In practice, it is often easier to consider radioactive decay in terms of a radioactive parent and radioactive progeny (daughter). **For any closed system, the number of progeny atoms plus the number of parent atoms remaining must equal the total number of parent atoms at the start. Solving for time considering these components yield the following equation: t = 1/ ln[1 + (P/N)] Where P = the number of progeny atoms produced.
- Slide 10
- The number of radioactive progeny can be determined from the following formula: P = N o (1 e - t ) With the passing of time, the radioactive parent atoms will decline and the radioactive progeny will increase.
- Slide 11
- If we take another look at the 238 U decay series, you can see that it isnt always as easy as one parent and one progeny Now what do we do? dN 2 /dt = 1 N 1 2 N 2 Where N 1 is the number of parent atoms and N 2 is the number of radiogenic progeny atoms. If 1 > 2, the amount of progeny will, at first, increase until the parent product has disappeared. Then the amount of progeny product will decrease.
- Slide 12
- Well, what if 1 < 2 ? A transient equilibrium will be reached. N 1 /N 2 = ( 2 1 )/ 1 If the half-life of the parent is much longer than the progeny, 1