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Published byElizabeth Arnold Modified over 2 years ago

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Do Now (3/17/14): What are some words and images that come to mind when you hear the word “radioactivity”? What is an isotope? What makes an isotope different than its element?

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Radioactivity 4/23/12

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Lesson Objectives Describe nuclear reactions and perform balancing of nuclear reactions by solving problems. Apply radioactivity equations by solving problems.

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Nuclear reaction A reaction in which the number of protons or neutrons in the nucleus of an atom changes.

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**Number of protons in the nucleus of the atom**

Atomic number Number of protons in the nucleus of the atom

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**Sum of protons and neutrons in the nucleus of the atom**

Mass number Sum of protons and neutrons in the nucleus of the atom

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Alpha decay Radioactive decay process in which the nucleus of an atom emits an alpha particle

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Alpha Particle Nucleus of a helium atom

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Beta decay Radioactive decay that occurs when a neutron is changed to a proton within the nucleus of an atom, and a beta particle and an antineutrino are emitted

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Gamma decay Radioactive process of decay that takes place when the nucleus of an atom emits a gamma ray.

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**http://library. thinkquest**

y/radioactivity.html

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Isotope Atomic nuclei having the same number of protons but different number of neutrons

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**All Elements Have Radioactive Isotopes**

All elements have more than one isotope Some isotopes of all elements are radioactive Some half-lives are so short that the isotope is not found naturally Radioactive Isotope display

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A Half-Life Is the Time Required for ½ the Atoms of a Substance to Undergo Radioactive Decay Applet Animation T1/2 = time for half the sample to disintegrate Assume T1/2 = 5 years Number of nuclei present at time t = 0: N0 = When t = 5 yrs, N = 50 t = 10 yrs, N = t = 20 yrs, N = 125. Calculate the half-life animation

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Applet Animation

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Half Life: Half-life: time needed for half of remaining mass of element to decay

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Example #1: Fermium-253 has a half-life of seconds. A radioactive sample is considered to be completely decayed after 10 half-lives. How much time will elapse for this sample to be considered gone?

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Decay Rate T1/2=half life λ=decay rate

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Example #2: The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, what is the decay rate of Zn-71?

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Mass remaining m=mass remaining Original mass

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Example #3: The half life of Zn-71 is 2.4 minute. If one had 100 g at the beginning, how many grams would be left after 7.2 minutes elapsed?

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Practice: Use the rest of class to work on the paper: Radioactivity; problems: #2,5,6, and 7

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Do Now (4/24/12): Pd-100 has a half-life of 3.6 days. If one had 6.02x1023 atoms at the start, how many atoms would be present

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Do Now (4/24/12): U-238 has a half-life of 4.46x109 years. How much U-238 should be present in a sample 2.5 x years old, if 2 grams were present initially?

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Using Logarithms

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Using Logarithms

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Using Logarithms Solving for λ:

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Using Logarithms Solving for t:

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**The Uranium Decay Series**

Decay series animation The only radium that exists today is that which is created as a result of the decay of uranium.

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Carbon-14 Production Neutron enters nucleus and kicks out a proton. 0n1 + 7N > 6C14 + 1p1

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**Carbon-14 Enters the Ecosystem**

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Carbon Dating Since living organisms continually exchange carbon with the atmosphere in the form of carbon dioxide, the ratio of C-14 to C-12 approaches that of the atmosphere. From the known half-life of carbon-14 and the number of carbon atoms in a gram of carbon, you can calculate the number of radioactive decays to be about 15 decays per minute per gram of carbon in a living organism.

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**Measuring the Age of Organic Matter**

A German tourist in the Italian Alps discovered the remains of the "Iceman" in the ice of a glacier in

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**Calculating the Iceman's Age**

The current activity per gram of carbon half what it would be if the Iceman were alive. Since the half-life of carbon-14 is about 5700 years, the Iceman's remains are about 5700 years old.

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**Radioactivity Equations**

N(t) = population at time t N(0) = population at time zero N0 = N(0) l = decay constant Example: N0 = 1000 l = 2 x 10-3 years -1 When will N = 200? N = N0 e-lt (1) e-lt = N /N0 (2) ln (e-lt) = ln (N /N0) (3) -l t = ln (N /N0) (4) N(t) = N0 e-lt t = - [ln (N /N0)] / l (5) = - [ln (200/1000)] /2 x10-3 (6) = 805 years

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Half-Life Problem The half-life of a radioactive substance is 10 hours. What is the decay constant, l? N = N0 e-lt (1) 0.50 N0 = N0 e-l10 (2) e-l10 = 0.50 (3) ln(e-l10) = ln(0.50) (4) -10 l = (5) l = hrs-1 (6)

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Half-Life Problem From the previous problem, how much time will it take for the sample's activity to fall to only 20% of what it was originally? N = 0.20 N0 (7) 0.20 N0 = N0 e t (8) t = ln (0.20) (9) t = 23 hours

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**Decay Constant and Half-Life**

N = N0 e-lt (1) N0 = N0 e-lT (2) (T = half-life) e-lT = 0.50 (3) ln(e-lT) = ln(0.50) (4) -lT = (5) T = 0.693/l (6) l = 0.693/T (7)

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Half-Life Example 38Sr90 (strontium-90) has a half-life of 28.5 years. How long will it take for 98% of a sample of strontium-90 to disappear? l = 0.693/T1/2 = / 28.5 = years-1 0.02 = e t t = - ln(0.02) / years-1 = 161 years

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Radioactivity Units A = number of disintegrations per second, activity A = lN One becquerel (Bq) is one disintegration per second. One curie is the number of disintegrations per second (the "activity") of one gram of radium, or about 3.7 x Bq.

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**Units of Absorbed Radiation**

Rad: 10 milli-joules per kilogram 20 rads of X-rays doesn't do the same damage to humans as 20 rads of alpha particles Rem: an absolute biological damage unit

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**Radiation Sickness Dose (rems) Effect 50-300 Sickness 400-500**

Lethal 50% (LD50) Above 600 Lethal 100% (LD100)

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**Calculate Rems from Rads (Relative Biological Effectiveness)**

Radiation R (rems/rad) a-particles 20 Neutrons 10 Protons b-particles 1 g-rays 1 X-rays Example: One joule of energy per kilogram is absorbed in the form of neutrons. Will this prove fatal? 1 rad is ten milli-joules 1 rad = J Example: How many rads of protons will kill a person? 600 rems is fatal RBE for protons is 10 Number of rads = 600 / 10 = 60

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Radon Poisoning Uranium in earth's crust decays to radium, which decays to radon. Radon is an odorless, tasteless, lighter-than-air gas which rises from the ground through cracks and fissures in the earth into homes. When breathed, the alpha- emitting radon can cause cancer of the lung. Radon is the single greatest source of radiations for humans, providing about 200 milli-rems per year per person.

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**Practice: Complete any four problems from the Radioactivity Worksheet**

When you are finished, raise your hand so I can stamp it Bring this paper to school with you this week!

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