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# Half-Life

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1. Half-Life

2. The number of particles decaying in a short period of time is proportional to the number of particles. The decay constant is l. The decay rate or activity is the rate of change. Activity decreases as time increases Decay Rates

3. Measured Activity • The SI unit of activity is the Becquerel (Bq). • equals one decay/sec (s-1) • The older unit is the curie (Ci). • Based on the decay of 226Ra • Once activity of one gram • Now defined by Bq • 1 Ci = 3.7  1010 Bq

4. Half-Life • The relationship for decay gives rise to an exponential relation. • Decay constant is fixed for a decay reaction • Decay is usually expressed as a half-life. • Time for half a sample to decay • Half-life constant for the nucleus type

5. Exponential Decay • Half-life applies to each sample separately. • This is exponential decay

6. A source of 24Na is marked at 1.16 MBq. Find the number of atoms of 24Na in the sample. Look up the half-life in a table. T = 15 h T = 5.4  104 s The activity is given in the problem. Related to decay constant and sample size Convert to half-life Sample Size

7. Physical variables are often normalized to the mass. Described as “specific” Specific activity is the activity of a sample divided by the mass. Units Bq g-1 or mCi g-1 In solution expressed per unit volume: pCi L-1 For a pure radionuclide: Normal soil has a few pCi/g Drinking water has a recommended limit of 5 pCi/L of 226Ra + 228Ra. Specific Activity

8. Figure 29.08 14C is a very rare isotope with a half-life of 5730 years. • In a living organism, the 14C activity is 0.25 Bq. • When the organism dies, the 14C exchange with the environment stops. • 14C starts decaying. • By measuring the 14C /12C ratio we can estimate the age of the sample.

9. Nuclear decay can leave a nucleus in an excited state. Many possible states may be reached Lifetime typically 10-10 s Excess energy may be lost as a photon or electron. Single gamma Series of gamma emissions Internal conversion beta Excited States 4.785 MeV 94.4%a 5.5%a 0.186 MeV 2.2% 3.3% b 0 MeV

10. Carbon-14 (14C) is a radioactive isotope. Beta decay Half-life 5730 years Carbon-14 is produced in the atmosphere by cosmic rays. Absorbed by organisms Stops at death Fraction of 14C to 12C establishes the date of an object. Radiocarbon next