Question

You are in a laboratory working with radioactive nuclei. When you leave for lunch, there are only 4,000 nuclei present which has a half-life of 10 minutes. When you return, only 250 nuclei remain. How long were you gone from the laboratory.

Answer 1

We can use the half-life formula to solve this problem:

N = N0 * (1/2)^(t/T)

where:
N = final number of nuclei (250)
N0 = initial number of nuclei (4,000)
t = time elapsed
T = half-life (10 minutes)

Substituting the given values into the formula:

250 = 4,000 * (1/2)^(t/10)

Dividing both sides by 4,000:

1/16 = (1/2)^(t/10)

Taking the logarithm of both sides (base 2):

log(1/16) = log[(1/2)^(t/10)]

-4 = (t/10) * log(2)

Solving for t:

t = -4 / log(2) * 10

t ≈ 13.86 minutes

Therefore, you were gone from the laboratory for approximately 13.86 minutes.