Question

The half-life of silicon-32 is 710 years. If 5 grams are present now, how much will be present in 1900 years? (Round your answer to three decimal places.)

A) 0.330 grams
B) 0.125 grams
C) 0.059 grams
D) 0.785 grams

Answer 1

The amount of silicon-32 remaining after 1900 years, based on a half-life of 710 years, is approximately 0.559 grams after performing the radioactive decay calculation, which is not listed in the provided options.

Step-by-step explanation:

To calculate the amount of silicon-32 that will be present after 1900 years, given its half-life of 710 years, we use the concept of radioactive decay. After each half-life, half of the substance remains. In 1900 years, there would be:

1. After the first 710 years, 2.5 grams remain.
2. After the second 710 years (1420 years in total), 1.25 grams remain.
3. 1900 years is 2.68 half-lives (1900/710), therefore we calculate the remaining amount by 5 grams × (1/2)^(2.68). This results in approximately 0.559 grams.

The closest answer after rounding to three decimal places is 0.559 grams, which is not listed among the provided options A) through D). Therefore, none of the given options is correct.