2. Lecture 34, PH101, Fall 2002 THE NUCLEUS: RADIOACTIVITY & HALF-LIFE

3. Zoom In to Nucleus THE NUCLEUS OF AN ATOM Atom: Electrons + Nucleus Enlarged view of the Nucleus Nucleus contains NUCLEONS: Protons: Positive Neutrons: Neutral (almost identical to the Proton, but for the charge)

4. Nuclear Forces There are two kinds of forces in the nucleus: Electrical Forces (Repulsive) Between positively charged protons. Strong Forces (Attractive) Between protons & neutrons. Always attractive. Does NOT depend upon charge. Strong forces are responsible for holding the nucleus together.

5. Why do some nuclei disintegrate? C Far apart Electrical repulsion dominates when two protons (A and C) are far apart. A B Close together Strong attraction dominate when two protons (A and B) are close together. So, in larger nuclei (e.g. Uranium) when the protons are more likely to be far apart, the electrical repulsion tends to dominate the strong attraction, causing the nucleus to disintegrate.

6. What is Radioactivity? The disintegration of a nucleus and release of several different kinds of rays and particles is called radioactivity. More energetic than X-Rays

7. After Alpha Decay A Uranium nucleus has a total mass of 238 nucleons and a charge +92. What is its mass and charge after one alpha decay? 1.Mass is 234, Charge is +88. 2.Mass is 236, Charge is +90. 3.Mass is 236, Charge is +92. 4.Mass is 234, Charge is +90. 5.None of above. In Alpha decay, you lose … 2 Protons + 2 Neutrons. i.e. you lose 4 nucleons, So, mass decreases by 4 units. New mass = 238 – 4 = 234 units. Proton alone has charge, and you lose 2. So, charge decreases by 2 units. New charge = 92 – 2 = +90

8. After Beta Decay A Thorium nucleus has a total mass of 234 nucleons and a charge +90. What is its mass and charge after one beta decay? 1.Mass is 234, Charge is +89. 2.Mass is 234, Charge is +91. 3.Mass is 233, Charge is +89. 4.Mass is 233, Charge is +91. 5.None of above. In Beta decay, you lose 1 electron. i.e. you lose NO nucleons, So, mass does NOT change. New mass = Old Mass = 234 units. Electron has charge of –1, So, when you lose an electron, new charge is increased by 1 unit. New charge = +90 – (– 1) = +91 [Hint: Electron mass is negligible, charge is -1]

9. How long does disintegration take? The rate at which an atom disintegrates is measured by its half-life. Half-Life is the time in which one-half of any number of nuclei will have disintegrated. E.g. Half-Life of Radium is 1,620 Years. If we start out with a certain amount of say 1kg, then … after 1,620 years we only have ½ kg. after another 1,620 years we have ¼ kg. after yet another 1,620 years we have 1/8 kg. After each half-life, we have half of what we had previously.

10. HALF - LIFE 1kg Weight of Radon Time 1/2 kg 1 x 1,620 Years (1/2) x 1kg = (1/2) kg 1 half life 1/4 kg 2 x 1,620 Years (1/2) x (1/2) x 1kg = (1/4) kg 2 half lives 1/8 kg 3 x 1,620 Years (1/2) x(1/2) x (1/2) x 1kg = (1/8) kg 3 half lives 1/16 kg 4 x 1,620 Years (1/2) x (1/2) x (1/2) x (1/2) x 1kg = (1/16) kg 4 half lives

11. Figuring Amount Left Over The half-life of Cobalt-60 is about 5 years. If you have 1kg of Cobalt-60 today, about how much of it would you have 15 years later? 1.1/16 kg. 2.1/8 kg. 3.1/6 kg. 4.1/4 kg. 5.1/3 kg. 15 years is 3 half-lives. So amount left over is: (1/2) x (1/2) x (1/2) x 1kg = 1/8 kg. 3 half-lives

12. 16 → 2 in ~ 9 days

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14. Figuring Half - Life You start out with a 1,000 of bacterial cells and 20 days later, you have only 250 of them still alive. What is the half- life of the bacterial cells? 1.4 days. 2.5 days. 3.10 days. 4.20 days. 5.Not enough info. 250 out of 1,000 is 1/4. (1/4) is the same as (1/2) x (1/2) So, it means 2 half-lives have passed. So: 20 days is 2 half lives. So, a half-life is 10 days.

15. Applications of Half – Life Carbon-14 Dating Every living organism contains a very small percentage of radioactive Carbon-14, which decays but is replenished from the Carbon-14 in the food. When the organism dies it no longer consumes Carbon-14. And Carbon-14 decays into Carbon-12, with a half-life of about 5,730 years. So, by measuring the percentage of Carbon-14 to Carbon-12 in a fossil of the organism it is possible to work backward and figure how long ago it lived.

16. Zone 1 counties have a predicted average indoor radon screening level greater than 4 pCi/L (pico curies per liter) (red zones) Zone 2 counties have a predicted average indoor radon screening level between 2 and 4 pCi/L (orange zones) Zone 3 counties have a predicted average indoor radon screening level less than 2 pCi/L (yellow zones) http://www.epa.gov/radon/zonemap.html

17. http://www.epa.gov/radon/zonemap/kansas.htm

18. Today’s lab – Zorkium data Plot Corrected Activity vs. Time. Perform an Automatic Curve Fit using the Natural Exponent fit y=A exp(-Cx) + B Calculate the effective half life of the daughter products of Ra-222 collected from the air on the balloon. Use the formula t 1/2 = ln(2)/C i.e. t 1/2 = 0.693/C Obtained value for the half life is in the same time units as units used to plot time on the graph. The constant C from the graph is known as the decay constant and is usually referred to as "lambda" (λ).

19. Today’s lab – Balloon data Plot Corrected Activity vs. Time. Perform an Automatic Curve Fit using the Natural Exponent fit y=A exp(-Cx) + B Calculate the effective half life of the daughter products of Ra-222 collected from the air on the balloon. Use the formula t 1/2 = ln(2)/C i.e. t 1/2 = 0.693/C Obtained value for the half life is in the same time units as units used to plot time on the graph. The constant C from the graph is known as the decay constant and is usually referred to as "lambda" (λ).

20. Today’s lab – Balloon data