
#1
Dec1206, 10:26 AM

P: 53

Does anyone know how to calculate the specific activity [Ci/g] for radionuclides from halflife times? (using to calculate activity, sources are encapsulated and cannot be opened)
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 Pu238, Pu239, Pu240, Pu241, Pu242, Am241) 



#2
Dec1206, 10:39 AM

Sci Advisor
P: 1,137

[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 halflife by: [tex]\lambda = { ln (2) \over \tau_{1/2}}[/tex] If you know the halflife 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 halflife, and atomic weight. Dr. Gregory Greenman Physicist 



#3
Dec1206, 11:06 AM

P: 53

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




#4
Dec1206, 05:05 PM

P: 395

Specific Activity
I am glad this came up. I was bored while preparing for my radiation physics final and I decided to find out how many kilograms of U238 are needed to have the same activity as one kilogram of Ra226. The answer I got was around 3 BILLION kilograms of U238. I may have made a mistake, and even though it was just for fun (Fun? What has school done to me?), I wouldn't mind someone double checking. See what you come up with, terfrr.




#5
Dec1206, 05:35 PM

P: 53

According to the software Im using it would take 2.97E+6 grams of U238. 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 Ra226 0.99885 [Ci/g] and SA U238 3.361E7 [Ci/g]), divided Ra/U for grams U assuming 1g Ra 



#6
Dec1306, 08:07 AM

Sci Advisor
P: 1,137

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 halflifes and atomic weights. Thereforre, the ratio of the specific activity will be given by the product of the proper ratios of the halflifes and atomic weights. The halflife of U238 is 4.468 Billion years; the halflife of Ra226 is 1600 years. The atomic weights are approximately 238 and 226, of course. If the halflife 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 U238 to Ra226 should be given by: Ratio = ( U238 halflife )/( Ra226 halflife ) * ( U238 atomic wt ) / ( Ra226 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 U238 to have the same activity as 1 kilogram of Ra226 Dr. Gregory Greenman Physicist 



#7
Dec1306, 11:06 PM

P: 395

I had used this to calculate. I should have thought of comparing the specific activities. [tex] A_{U238} = \lambda N = A_{Ra226}[/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? 



#8
Dec1406, 07:01 AM

Admin
P: 21,634

Comparing 4.468 Billion years to 1600 years  that's 6 orders of magnitude.
The ratio of U238 to Cs137 or Sr90 is even greater, 8 orders of magnitude. Then there are radionuclides that have halflives 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 halflife, 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
Dec1406, 08:13 AM

Sci Advisor
P: 1,137

As Astronuc points out  the huge ratio in the specific activities of these radionuclides is almost entirely due to the huge ratio in halflives. Basically, U238 is ALMOST stable!! It has a halflife of about 4.5 BILLION years which is roughly the age of the Earth. So only one U238 halflife has elapsed since the Earth was formed. If U238 was stable, the halflife would be INFINITE. Then your specific activity ratio would be a lot bigger!!! Dr. Gregory Greenman Physicist 



#10
May2111, 03:44 PM

P: 1

How do i calculate the activity of Th234 that i would expect to find in a 0.25g sample of Uranyl nitrate (UO2(NO3)2.6H2O) and what mass of Th234 is this activity equivalent to?




#11
Jun2711, 10:17 AM

P: 82

Specific activity data for radionuclides is given on Wolfram Alpha... just look up whatever nuclide you like.
But I guess understanding how you can calculate it from halflife is a good thing to understand, anyhow :) 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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