The hot potato

A nuclear physicist with a demented sense of humor tosses you a cigar box, yelling "hot potato." The label on the box says "contains 10²⁰ atoms of ¹⁷F, half-life of 66 s, produced today in our reactor at 1 p.m." It takes you two seconds to read the label, after which you toss it behind some lead bricks and run away. The time is 1:40 p.m. Will you die?

The time elapsed since the radioactive fluorine was produced in the reactor was 40 minutes, or 2400 s. The number of elapsed half-lives is therefore t/t_1/2 = 36. The initial number of atoms was N(0) = 10²⁰ . The number of decays per second is now about 10⁷ s^-1, so it produced about 2 × 10⁷ high-energy electrons while you held it in your hands. Although twenty million electrons sounds like a lot, it is not really enough to be dangerous.