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![Page 1: Do Now (3/17/14): 1. What are some words and images that come to mind when you hear the word “radioactivity”? 2. What is an isotope? 3. What makes an isotope.](https://reader035.fdocuments.us/reader035/viewer/2022062518/56649cdc5503460f949a6c04/html5/thumbnails/1.jpg)
Do Now (3/17/14):
1.What are some words and images that come to mind when you hear the word “radioactivity”?
2.What is an isotope?
3.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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Atomic number
Number of protons in the nucleus of the atom
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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.org/17940/texts/radioactivity/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 attime t = 0:
N0 = 1000---------------------------------------When t = 5 yrs, N = 50 t = 10 yrs, N = 250 t = 20 yrs, N = 125.
Calculate the half-life animation
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Half Life:
Half-life: time needed for half of remaining mass of element to decay
t (# halflives)T12
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Example #1:
Fermium-253 has a half-life of 0.334 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
0.693
T12
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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
m m0e t
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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 x10 10 years old, if 2 grams were present initially?
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Using Logarithms
m m0e t
m
m0e t
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Using Logarithms
m
m0e t
lnm
m0
t
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Using Logarithms
Solving for λ:
lnm
m0
t
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Using Logarithms
Solving for t:
t lnm
m0
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The Uranium Decay Series
The only radium that exists today is that which is created as a result of the decay of uranium.
Decay series animation
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Carbon-14 Production
Neutron enters nucleus and kicks out a proton. 0n
1 + 7N14 ---------> 6C
14 + 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 theItalian Alps discoveredthe remains of the "Iceman" in the ice of aglacier in 1991.
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Calculating the Iceman's Age
The current activity per gram ofcarbon half what it would be ifthe Iceman were alive.
Since the half-life of carbon-14is about 5700 years, theIceman's remains are about5700 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
N(t) = N0 e-lt
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) 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 is10 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 = -0.693 (5) l = 0.0693 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-0.0693 t (8)
-0.0693 t = ln (0.20) (9)
t = 23 hours
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Decay Constant and Half-Life
N = N0 e-lt (1)
0.50 N0 = N0 e-lT (2)
(T = half-life) e-lT = 0.50 (3)
ln(e-lT) = ln(0.50) (4) -lT = -0.693 (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
= 0.693 / 28.5 = 0.0243 years-1
0.02 = e-0.0243 t t = - ln(0.02) /0.0243 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 10 10 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 20rads 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 10
b-particles 1
g-rays 1
X-rays 1
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
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 = 0.010 J
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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!