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Or, does anyone know of somewhere on the net the actual numerical values for each nuclide are? Neither my textbooks nor google has turned up anything useful for me. (In specific, Im looking for Pu-238, Pu-239, Pu-240, Pu-241, Pu-242, Am-241)

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- Thread starter tehfrr
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- #1

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Or, does anyone know of somewhere on the net the actual numerical values for each nuclide are? Neither my textbooks nor google has turned up anything useful for me. (In specific, Im looking for Pu-238, Pu-239, Pu-240, Pu-241, Pu-242, Am-241)

- #2

Morbius

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Or, does anyone know of somewhere on the net the actual numerical values for each nuclide are? Neither my textbooks nor google has turned up anything useful for me. (In specific, Im looking for Pu-238, Pu-239, Pu-240, Pu-241, Pu-242, Am-241)

Quite simple. The rate at which a nuclide decays is given by the formula:

[tex]{ dN \over dt} = -\lambda N[/tex]

where N is the number of radioactive nuclei, and lambda is the decay constant, which

is related to the half-life by:

[tex]\lambda = { ln (2) \over \tau_{1/2}}[/tex]

If you know the half-life you can calculate lambda. To get the number of radioactive

nuclei, N; if you know the mass; calculate the number of moles by dividing the mass

by the atomic weight of the nuclide. Multiply by Avogadro's Number to get N.

Now you can calculate the decay rate in terms of decays per second.

To convert to Curies, note that a Curie is defined as 3.7e+10 decays per second:

http://en.wikipedia.org/wiki/Curie

Divide by the mass; and you have the specific activity. Note that if you leave the

mass out of the step above where you calculate the number of moles; then you don't

have to divide by it later. So you will have specific activity in terms of half-life, and

atomic weight.

Dr. Gregory Greenman

Physicist

- #3

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That should work since I have the mass. Thank you.

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- #5

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According to the software Im using it would take 2.97E+6 grams of U-238. When I go home Ill try it by hand using Morbius' method and see if I come up with the same number.

(software gives SA Ra-226 0.99885 [Ci/g] and SA U-238 3.361E-7 [Ci/g]), divided Ra/U for grams U assuming 1g Ra

(software gives SA Ra-226 0.99885 [Ci/g] and SA U-238 3.361E-7 [Ci/g]), divided Ra/U for grams U assuming 1g Ra

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- #6

Morbius

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Candyman,

I think you slipped a few decimal points; it's about 3 MILLION.

The calculation as I outlined above; if you take the mass out, so that you are calculating

specific activity; depends on the half-lifes and atomic weights. Thereforre, the ratio

of the specific activity will be given by the product of the proper ratios of the half-lifes

and atomic weights.

The half-life of U-238 is 4.468 Billion years; the half-life of Ra-226 is 1600 years.

The atomic weights are approximately 238 and 226, of course.

If the half-life is longer; then you need more of the substance for a given activity.

Likewise, if the atomic weight is larger, you have fewer nuclei per unit mass.

Therefore the ratio of the specific activities of U-238 to Ra-226 should be given by:

Ratio = ( U-238 half-life )/( Ra-226 half-life ) * ( U-238 atomic wt ) / ( Ra-226 atomic wt )

= ( 4.468e9 / 1600 ) * ( 238 / 226 ) = 2.94e+06

[This is essentially what tehfrr got with his software.]

So it takes 3 Million kilograms of U-238 to have the same activity as 1 kilogram of Ra-226

Dr. Gregory Greenman

Physicist

- #7

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I think you slipped a few decimal points; it's about 3 MILLION.

I see, I forgot to convert grams to kilograms after I found the moles of U-238 needed.

I had used this to calculate. I should have thought of comparing the specific activities. :grumpy:

[tex] A_{U-238} = \lambda N = A_{Ra-226}[/tex]

Still, I am astounded by these huge numbers! If I did not do the calculation myself, I would disbelieve such a claim. Has anyone else been suprised by how the numbers turn out?

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- #8

Astronuc

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The ratio of U-238 to Cs-137 or Sr-90 is even greater, 8 orders of magnitude.

Then there are radionuclides that have half-lives of months, weeks, days, hours and seconds. The short the half life, the greater the specific initial or equilibrium specific activity. However, the shorter the half-life, the faster the particular radionuclide decays. On the other hand, that may mean decaying into another radionuclide of longer half life, before decaying into an inert isotope.

- #9

Morbius

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Candyman,Still, I am astounded by these huge numbers! If I did not do the calculation myself, I would disbelieve such a claim. Has anyone else been suprised by how the numbers turn out?

As Astronuc points out - the huge ratio in the specific activities of these radionuclides is

almost entirely due to the huge ratio in half-lives.

Basically, U-238 is ALMOST stable!! It has a half-life of about 4.5 BILLION years which

is roughly the age of the Earth. So only one U-238 half-life has elapsed since the Earth

was formed.

If U-238 was stable, the half-life would be INFINITE. Then your specific activity ratio

would be a lot bigger!!!

Dr. Gregory Greenman

Physicist

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- #11

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But I guess understanding how you can calculate it from half-life is a good thing to understand, anyhow :)

We need to either get some more data here or take some assumptions.

What's the uranyl nitrate isotopic composition? Natural? Depleted?

Can we assume that the uranium daughter products are all in secular equilibrium?

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