Question

Calculate the amount of americium-241 consumed in a smoke detector (initially containing 5.0000 µg of Am), in micrograms, that has been used for 1.000 year if the half-life is 433 years.

Answer 1

The amount of americium-241 consumed in a smoke detector after 1 year is 0.0023 µg, calculated using the half-life formula and the given initial amount of 5.0000 µg of americium-241.

Step-by-step explanation:

To calculate the amount of americium-241 consumed in a smoke detector after 1.000 year, we use the concept of half-life, which in this case, is provided as 433 years.

The initial amount of americium-241 in the smoke detector is 5.0000 µg. Using the formula for exponential decay, N(t) = N0 * 0.5^(t/T), where N(t) is the remaining amount after time t, N0 is the initial amount, t is the time elapsed, and T is the half-life.

Here, N0 = 5.0000 µg,

t = 1 year,

and T = 433 years.

Substituting the values, we get N(t) = 5.0000 µg * 0.5^(1/433)

= 4.9977 µg.

The amount of americium-241 consumed is therefore the initial amount minus the remaining amount, which equals 5.0000 µg - 4.9977 µg = 0.0023 µg.