Radioactive Milk

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Milk contains enough radioactive potassium-40 to set a Geiger Counter humming. But it didn't come from Fukushima, or any human activity.

Big Ideas: 
  • Nucleosynthesis: most nuclei were made just before the solar system was formed, and not enough time has elapsed for some radioactive species to decay.

  The Human Health Fact Sheet from the Argonne National laboratory in Illinois1 has a page on potassium-40 (40K); it states "It is the predominant radioactive component in human tissues and in most food.  For example, milk [typically] contains about 2,000 pCi/L of natural potassium-40".   

  What does 2,000 pCi/L mean? The curie (Ci) is the old measure of (radio)activity, and means 37 billion decays per second (3.7 x 1010 Bq). 

  2000 x 10-12 Ci/L =( 2000 x 10-12 Ci)(3.7 x 1010 Bq/Ci) = 74 Bq

  In other words, in 1L of milk, 74 radioactive 40K nuclei decay each second. So how much 40K is in there to start with?

  The half life of 40K is 1.28 billion years. In other words however much was made in the last round of supernova explosions that made the material for our solar system about 4.6 billion years ago, a little more than 8% (i.e. 2-4.6/1.28) of the original is left. In fact it makes up 0.012% of all potassium (that's about one radioactive potassium atom per 8000 stable atoms), and potassium is a very common element. An average 70 kg human body contains about 140 g of potassium, i.e. about 17 mg of 40K.

  The mean life of 40K (denoted by the Greek tau, τ) is:

  τ = 1.28/0.693 = 1.85 billion years = (1.85 x 109 y)(3.15 x 107 s/y) = 5.82 x 1016 s.

  The activity, A = N/τ, where N is the number of nuclei present. For 1L of milk:  

  N = A τ = (74 Bq)(5.82 x 1016 s) = 4.31 x 1018 nuclei.

  The mass of this many 40K nuclei = (40)(1.66 x 10-27 kg)(4.31 x 1018) = 2.9 x 10-7 kg ≈ 0.3 mg (per L, or per kg).

  This is almost the same as the mass of 40K in every kg of our bodies (0.2% K)(0.012% 40K/K) = 2.4 x 10-7 kg 40K per kg.

  Our total radiation dose from 40K in our own bodies is about 0.17 mSv/y2. Our total natural dose is a few mSv/y.














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