A Geiger counter registers a count rate of 8,000 counts per minute from a sample of a radioisotope.The count rate 24 minutes later is 1,000 counts per minute.The half-life of the radioisotope is 8 minutes.

Question

Quizplus · Accepted Answer

The count rate decreasing from 8,000 to 1,000 counts per minute in 24 minutes indicates that the number of radioactive atoms (and thus the count rate) is decreasing at a rate proportional to the initial count rate.

Using the formula N(t) = N0 * (1/2)^(t/T), where N0 is the initial number of radioactive atoms, t is the elapsed time, and T is the half-life, we can solve for T:

1000 = 8000 * (1/2)^(24/8)

1000/8000 = (1/2)^3

1/8 = 1/8

Therefore, the half-life of the radioisotope is indeed 8 minutes.

A Geiger Counter Registers a Count Rate of 8,000 Counts