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**CHAPTER 28 Nuclear Chemistry**

Radioactive Decay

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**Nuclide = atom of an isotope**

A. Nuclear Stability Nuclide = atom of an isotope

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A. Nuclear Stability Nuclear stability – stable nuclei always have at least as many neutrons as protons.

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A. Nuclear Stabiity For an odd/even or even/odd nucleus, if the mass number is different by more than 1 amu from the rounded atomic mass, the nuclide is unstable. Ex:

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A. Nuclear Stability For an even/even nucleus, if the mass number is different by more than 3 amu from the rounded atomic mass, the nuclide is unstable. Ex:

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A. Nuclear Stability For odd/odd nuclei, only four stable isotopes are found in nature:

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**B. Nuclear Decay 2+ 1- 1+ Alpha particle () helium nucleus**

paper 2+ Beta particle (-) electron 1- lead Positron (+) positron 1+ concrete Gamma () high-energy photon

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**B. Nuclear Decay Top and bottom numbers must balance!! Alpha Emission**

parent nuclide daughter nuclide alpha particle Top and bottom numbers must balance!!

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B. Nuclear Decay Beta Emission electron Positron Emission positron

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**B. Nuclear Decay Electron Capture electron Gamma Emission**

Usually follows other types of decay. Transmutation Atom of one element changes into an atom of another element.

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**B. Nuclear Decay Why nuclides decay…**

need stable ratio of neutrons to protons DECAY SERIES TRANSPARENCY

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**C. Half-life Half-life (t½)**

Time required for half the atoms of a radioactive nuclide to decay. Shorter half-life = less stable.

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C. Half-life mf: final mass mi: initial mass n: # of half-lives

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**C. Half-life t½ = 5.0 s mf = mi (1/2)n mi = 25 g mf = (25 g)(0.5)12**

Fluorine-21 has a half-life of 5.0 seconds. If you start with 25 g of fluorine-21, how many grams would remain after 60.0 s? GIVEN: t½ = 5.0 s mi = 25 g mf = ? total time = 60.0 s n = 60.0s ÷ 5.0s =12 WORK: mf = mi (1/2)n mf = (25 g)(0.5)12 mf = g

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C. Half-life Nt: final mass N0: initial mass t: elapsed time

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C. Half-life k: rate constant t1/2: half-life

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**C. Half-life t½ = 11.4 days k = 0.693 / t1/2 k = 0.693 / 11.4 days**

A sample of radium-223 has a half-life of 11.4 days. What is the rate constant for this isotope? GIVEN: t½ = 11.4 days WORK: k = / t1/2 k = / 11.4 days k = days -1

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**C. Half-life k = 0.035 yr -1 k = 0.693 / t 1/2 t ½ = 0.693 / k**

The rate constant for gold-200 is /year. What is the half-life of gold-200? GIVEN: k = yr -1 WORK: k = / t 1/2 t ½ = / k t ½ = / yr -1 t ½ = yr ≈ 20. years

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**C. Half-life t ½ = 1.7 x 107 yr ln (N0/Nt) = kt N0 = 3.75 g**

The half-life of iodine 129 is 1.7 x 107 years. If a nuclear bomb explosion resulted in 3.75 g of iodine-129, how much time would have to elapse for the amount of iodine-129 to be 0.75 g? GIVEN: t ½ = 1.7 x 107 yr N0 = 3.75 g Nt = 0.75 g t = ? WORK: ln (N0/Nt) = kt ln (3.75/0.75) = 0.693/1.7 x 107 t t = 3.9 x 107 years (39, 000, 000 years!)

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D. Radiocarbon Dating Carbon-14 is in all living things through the carbon cycle. Amount of carbon-14 stays constant until organism dies, then it begins to decay.

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D. Radiocarbon Dating Amount of carbon-14 can be expressed as either a percentage or as a decimal number. Example: amount of carbon-14 in a dead tree could be expressed as 38% or 0.38 of the original amount.

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**Half-life of carbon-14 : 5730 years**

D. Radiocarbon Dating Half-life of carbon-14 : years

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D. Radiocarbon Dating The remnants of an ancient canoe are found in a cave in northern Australia. The amount of carbon-14 is 6.28 counts per minute, and the amount of carbon-14 in a tree today is 13.6 counts per minute. What is the approximate age of the canoe?

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**D. Radiocarbon Dating t ½ = 5730 yr k = 0.693 / 5730 yr**

GIVEN: t ½ = 5730 yr N0 = 13.6 cts/min Nt = 6.28 cts/min t = ? WORK: k = / 5730 yr k = x 10-4 yr -1 ln (N0/Nt) = kt ln (13.6/6.28) = x 10-4 t t = years 2011 – 6390 = 4379 BC

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E. Fission Occurs when isotopes are bombarded with neutrons and split the nucleus into smaller fragments, accompanied by the release of neutrons and a large amount of energy. (Each atom can capture 1 neutron.)

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E. Fission Chain reaction – occurs when atomic nuclei that have split release energetic neutrons that split more nuclei.

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**E. Fission Two steps in controlling fission:**

Neutron moderation – water or carbon slows down the neutrons Neutron absorption – decreases the number of slow neutrons through the use of control rods made of neutron-absorbing materials (usually cadmium)

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F. Fusion Occurs when two light nuclei combine to produce a nucleus of heavier mass, accompanied by the release of a large amount of energy.

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**F. Fusion Occurs in all stars**

High temperatures are necessary to initiate fusion (no cold fusion yet) Possible future energy source Hydrogen bomb is a fusion reaction (fusion of two deuterium nuclei).

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**G. Methods of Detection Geiger Counters (primarily beta)**

Scintillation counter – coated screen detects radiation particles. Film badge – several layers of photographic film encased in a holder. Detects beta and gamma.

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**H. Radioisotopes in Medicine**

X-rays: Useful in imaging soft-tissue organs. Tracers: Iodine-131 is used to check for thyroid problems Radiation treatment: Some cobalt isotopes are used as radiation sources to treat cancer.

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