Question 23.95

65. You are radioactive! So are bananas. Your body and bananas both contain potassium. (But you are fine because your body excretes it.) The half-life of potassium-40 is 1.25 billion years. (Fortunately, the biological half-life in you is only about two weeks.)

  1. What is the decay constant for potassium-40, in proportion per year? This is the tiny proportion that decays per year.
  2. What is the decay constant for potassium-40, in proportion per second? This is the very tiny proportion that decays per second.
  3. A typical banana contains about 450 mg of potassium, of which 0.0117% is radioactive potassium-40. Every 40 grams of potassium-40 is composed of atoms (i.e., Avogadro’s number of atoms) of potassium-40. How many decays per second of potassium-40 does a banana experience? [The dose of radiation from eating a banana is known as a banana equivalent dose (BED). The average daily exposure to radiation from all sources is about 100 BED, while a chest CT scan delivers 70,000 BED.]

65.

(a)

(b)

(c) 14/sec