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Table of nuclidesZ = # of protons

(A - Z) = # of neutrons

Stable nuclides: Z ~ A/2

How did they get made?

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*****Nuclear Structure*****

The only stable isotope of aluminum is 1327Al.

How many neutrons and protons are in the aluminum nucleus? How many electrons are in the neutral aluminum atom?

(14 neutrons, 13 protons, 13 electrons)

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Table of nuclides

Zn, Se, Cu, Mo, Ni, Sn

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Crab Nebula

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*****Explanation of the Crab***** The Crab Nebula, filled with mysterious filaments, is the result of a star that was seen to explode in 1054 AD. This spectacular supernova explosion was recorded by Chinese and (quite probably) Anasazi Indian astronomers. The filaments are mysterious because they appear to have less mass than expelled in the original supernova and higher speed than expected from a free explosion. In the above picture taken recently from a Very Large Telescope, the color indicates what is happening to the electrons in different parts of the Crab Nebula. Red indicates the electrons are recombining with protons to form neutral hydrogen, while blue indicates the electrons are whirling around the magnetic field of the inner nebula. In the nebula's very center lies a pulsar: a neutron star rotating, in this case, 30 times a second. (It

(The Crab nebula is about 6,500 light years away.)

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Nuclear Decays• Alpha emission

– Alpha = helium nucleus = 2 protons + 2 neutrons– Z changes by 2, A by 4

• Beta emission– Beta = electron or positron– Z changes by one, A stays the same

• Gamma emission– Gamma = photon = “particle of light”– Neither A nor Z change

• Neutron emission– A changes but not Z

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*****Some nuclear decays*****

What are the daughter nuclides for the following (probably unphysical) decays? Go to table to find your way around.

Alpha decay of B12? (B = boron)

Neutron decay of O19?

Beta (electron) decay of N16? (N = nitrogen)

Positron decay of C11?

(Li8, O18, O16, B11)

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n p + e-

Radioactive Carbon

C14 N14 + e-

678

54

{e- = electron}

How did we get electrons in the nucleus??

p n + e+

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How radioactive are you?

• How many carbon atoms are in you?– Maybe 1 kg of you is carbon???????

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How radioactive are you?

• How many carbon atoms are in you?– 6 x 1023 atoms/mole x 1 kg of carbon x

(1000/12) moles/kg = 5 x 1025 carbon atoms

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How radioactive are you?

• How many carbon atoms are in you?– 5 x 1025 carbon atoms

• How many of these are C14?– Only 1 in 1012 is C14

or 5 x 1013 C14 atoms

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How radioactive are you?

• How many carbon atoms are in you?– 5 x 1025 carbon atoms

• How many of these are C14?– 5 x 1013 C14 atoms

• How many of these decay each second?– About half decay in 5,000 years

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How radioactive are you?

• How many carbon atoms are in you?– 5 x 1025 carbon atoms

• How many of these are C14?– 5 x 1013 C14 atoms

• How many of these decay each second?– 2.5 x 1013 atoms x (1/5,000 years)

x (1/[3 x 107 seconds/year]) x 1.4 = 250 per second

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How radioactive are you?• How many carbon atoms are in you?

– 5 x 1025 carbon atoms

• How many of these are C14?– 5 x 1013 C14 atoms

• How many of these decay each second?– 250 (or 7 x 109 in a year!!!)

• Why aren’t we all dead? Or at least glowing in the dark?

• Dose is < 10-3 of average from all sources

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Radioactive decay• How fast does C14 go to N14?• Watch one atom

– Never see decay in progress– C14 for a while, then suddenly is N14

• Watch many atoms, initially all C14– See only mixture of C14 and N14 atoms– Early on, mostly C14 – Later, mostly N14– After very long wait, only N14

• t1 = t2 = t3 = T1/2

• Time for 1/2 to decay = half life– {= 5730 years for C14}

C14

N14

t1

t2

t3

??

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Simulations of N17 and O21 decays

Go to the Simulation

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Example from WebBe-11

B-11

Be

B

Nt =N0(12)

t/T1/ 2 =N0e−t/Tm : Tm =1.443T1/2

(decay rate of Be) = (1/Tm) x (number of Be)

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Example from WebBe-11

B-11

Be

B

Nt =N0(12)

t/T1/ 2 =N0e−t/Tm : Tm =1.443T1/2

(decay rate of Be) = (1/Tm) x (number of Be)

Curve NOT smoothCurve VERY “noisy” at long timesCurve NOT same on successive runsCurve does NOT go through 1/2 at t = T1/2

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*****Decay and Half-lives*****If I start with 1024 radioactive atoms that decay with a half life of ten minutes, how many are left after a half an hour?

If I start with 1024 radioactive atoms and after two hours I have only 16 left, what is their half life?

If I start with 1024 radioactive atoms and there are 256 left after an hour, how many will be left after two hours?

If I start with 106 radioactive atoms and there are 104 left after an hour, how many will be left after two hours? After three hours?

(128, 20 minutes, 32, [102, 1])

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C-14 Dating

• Physicist’s first (1950s) look at problem– Source of C-14– Distribution

– Organic content while alive = R0

– Decay of C-14/C-12 ratio after death, Rt

– Time since death t = T1/2 log2(R0/Rt)

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*****C14 dating links*****• Here’s a fun place to start

• Go to this site, click on radiocarbon at the left, and explore the several topics there.

• This one gives a LOT of more detailed information if you found not enough at the one above. As in the first, it may take some prowling around to find what you want.

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Upper Atmosphere—Source of C-14

Cosmic ray

junk

neutron

N-14

proton

C-14 O2

CO2

Nucleus of anything

Production rate: 2 atoms/second-cm2

7.5 kg/yr

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Atmospheric/oceanic mixing2%

98%

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Steady state C14 concentration

generation decay

New C14 Lost C14

atmosphere

oceans

C12 and C14

Atmospheric ratio R0 = C14/C12 = 1.2 x 10-12

C14 concentration adjusts until generation rate = decay rate:

gives

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Living organisms

C12

C14

Living organisms exchange with atmosphere to giveratio R0 = C14/C12 = 1.2 x 10-12

in tissues of the organism

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t years after death• NO CO2 exchange with atmosphere

• C12 is stable• C14 decays

• Ratio at time t is reduced to Rt with Rt = C14/C12 at time t = R0 (1/2)t/T (T = T1/2) = R0 e-t/T (T = Tm)

• t = T1/2 log2(R0/Rt)= Tm ln(R0/Rt) with T1/2 = 5568 years or Tm = 8033 years

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“Radiocarbon Age”

• Follow this procedure, result quoted as:

• radiocarbon age = t - {(date of experiment) - 1950} BP

• BP = “before present”

• “present” = 1950

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*****radiocarbon age*****

• 1) If a dating experiment is performed in the year 2000 and gives a t = 750 years, what is the “radiocarbon age”? And what is the apparent (uncalibrated) calendar age of the sample?

• 2) Try again, now with a dating experiment in 1975 which gave a t of 2500 years.

• 1) 700 years BP and 1250 years AD• 2) 2475 years BP and 525 years BC

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FRIDAY

• BRAINSTORMING SESSION–

WHAT MIGHT GO WRONG WITH THIS SCHEME??