A friend of yours has recently read a story on the Web that eating a broccoli should be avoided because broccoli contains potassium which has radioactive isotope K-40. As a consequence of reading this story, she has been telling you and others not to eat broccoli. Is eating broccoli, indeed, a radioactive hazard to your health? Determine the activity (in Bq or mCi) for a typical serving of broccoli which contains about 300 mg of potassium. Note that the natural abundance of K-40 is .0117% and its half life is T1/2=1.248E9 yr. Assuming the average radiation energy released per decay is 480keV, what is the maximum energy absorbed into one's body over 30 days, the time for 50% of the potassium-40 to be eliminated the body biologically. Do you agree with your friend that eating broccoli is a radioactive health risk?
Explanation / Answer
Given mass of potassium m = 300 mg number of moles n = 0.3g / 40 = 0.0075 number of nucleons N = 0.0075*6.02*1023 nucleons = 4.515*1021 nucleons half life of potassium is T 1/2 = 1.248*109 yr activity A = N = ( 0.693 / T 1/2 ) N = 0.693 * 4.515*1021 / 1.248*109 = 2.50 *1012 decays / year = 7.92744*104 decyas / sec = 7.92744*104 decyas / sec