a radioactive material produces 1390 decays per minute at one time, and 4.1 h later produces 150 decays per minute. What is its half-life?

To determine the half-life of a radioactive substance, we need to determine the time it takes for the number of decays per minute to decrease by a factor of two.

You can set up an expression that relates decays per minute at two time points.

1390 decays/min ×(1/2)^(t/(half-life)) = 150 decays/min

where t is the elapsed time between two measurements (4.1 hours) and (1/2)^(t/(half-life)) is the decay factor, dividing the number of decays per minute by half. reduce to

By rearranging the equation, we can solve for the half-life.

half-life = t ×log(2) / log((1390/150)^(1/t))

Substituting the values of t and the number of decays per minute at the two time points, we get

half-life = 4.1 ×log(2) / log((1390/150)^(1/4.1))

This simplifies to:

half-life = 4.1 × 0.693 / log (9.27)

=2.747 hours.

Therefore, the half-life of radioactive material is about 2.75 hours.