Question

The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the level of cobalt radiation in a certain region at 100 times the level acceptable for human habitation. How long will it be until the region is again habitable?

Answer 1

Answer:

  35 years

Step-by-step explanation:

The proportion p that remains after y years is ...

  p = (1/2)^(y/5.27)

In order for 1/100 to remain (the level decays from 100 times to 1 times), we have ...

  .01 = .5^(y/5.27)

  log(0.01) = y/5.27·log(0.5) . . . take logs

  y = 5.27·log(0.01)/log(0.5) ≈ 35.01 ≈ 35 . . . . years