Question

A radioactive element, Tungsten W-187 decays about 50% per day. Estimate about what percentage of the Tungsten W-187 decays per hour?

a. 3%
b. 97%
c. 2%
d. 98%

Answer 1

About 3% of Tungsten W-187 decays per hour, which is approximated using the formula for exponential decay and corresponds to option (a).

Step-by-step explanation:

To estimate the percentage of Tungsten W-187 that decays per hour when it decays 50% per day, we can use the formula for exponential decay:

N(t) = N_0 (1/2)^(t/T)

where:

• N(t) is the remaining quantity of substance after time t,
• N_0 is the initial quantity of substance,
• T is the half-life of the substance.

Since we are looking for an hourly decay rate and there are 24 hours in a day, we can set t = 1/24. To find the hourly rate, we set:

1/2 = (1 - hourly decay rate)^(24)

Solving for the hourly decay rate gives us approximately 0.029, or 2.9%. This estimation means that about 3% of Tungsten W-187 decays per hour, which corresponds to option (a).