Question

That same evil scientist guy has created yet another doomsday device. His trigger mechanism is a radiation counter that is pointed at a compound containing cobalt-55 (half-life of 17.5 hours). The counter reads 983 counts initially. If the evil scientist wants the mechanism to trigger in 44.0 hours, what should the trigger value be (i.e., the count value after 44.0 hours)?That same evil scientist guy has created yet another doomsday device. His trigger mechanism is a radiation counter that is pointed at a compound containing cobalt-55 (half-life of 17.5 hours). The counter reads 983 counts initially. If the evil scientist wants the mechanism to trigger in 44.0 hours, what should the trigger value be (i.e., the count value after 44.0 hours)?

Answer 1

The trigger value for the radiation counter after 44.0 hours should be approximately 369 counts.

Step-by-step explanation:

The trigger value for the radiation counter after 44.0 hours can be calculated using the half-life of the cobalt-55 isotope.

Since the half-life of cobalt-55 is 17.5 hours, we need to determine how many half-lives occur in 44.0 hours.

The number of half-lives can be found by dividing the total time (44.0 hours) by the half-life (17.5 hours):

Number of half-lives = 44.0 hours ÷ 17.5 hours

= 2.51 half-lives

Since each half-life cuts the count value in half, we can calculate the trigger value by multiplying the initial count value (983 counts) by 0.5 raised to the power of the number of half-lives:

Trigger value = 983 counts × (0.5)^2.51

≈ 369 counts