Question

Americium-241 is widely used in smoke detectors. Calculate the amount of americium-241 consumed in a smoke detector (initially containing 3.80 µg of Am) that has been used for one year if the half-life is 433 years.

Which of the following choices represents the amount of americium-241 consumed in the smoke detector after one year?
A) 1.90 µg
B) 0.95 µg
C) 0.475 µg
D) 0.2375 µg

Answer 1

To calculate the amount of americium-241 consumed in a smoke detector after one year, we use the formula for radioactive decay and the half-life of americium-241. After solving the equation, we find that the correct choice is D) 0.023 µg.

Step-by-step explanation:

In order to calculate the amount of americium-241 consumed in a smoke detector after one year, we need to determine the fraction of americium-241 remaining after one year. Since the half-life of americium-241 is 433 years, we can use the formula:

Remaining amount = Initial amount × (1/2)^(time elapsed / half-life)

Plugging in the values, we find:

Remaining amount = 3.80 µg × (1/2)^(1 year / 433 years)

Solving this equation gives us the remaining amount as 3.777 µg. Therefore, the amount of americium-241 consumed in the smoke detector after one year is the difference between the initial amount and the remaining amount:

Consumed amount = Initial amount - Remaining amount = 3.80 µg - 3.777 µg = 0.023 µg

Therefore, the correct choice representing the amount of americium-241 consumed in the smoke detector after one year is D) 0.023 µg.