Question

The half-life of Po-214 is 0.001 seconds. How much of a 10-gram sample is left after 0.003 seconds?

Answer 1

After 3 half-lives (0.003 seconds), a 10-gram sample of Polonium-214 (Po-214) decays to 1.25 grams.

Step-by-step explanation:

The half-life of an isotope is the time taken for half of a radioactive substance to decay. In the case of Polonium-214 (Po-214), the half-life is 0.001 seconds. To calculate the amount of material left after a given time period, we can use the formula for exponential decay, taking into account the number of half-lives that have passed.

The number of half-lives that have passed in 0.003 seconds is 0.003 / 0.001 = 3 half-lives. After each half-life, the sample size is halved. Therefore, after 3 half-lives, the sample size is halved three times.

Starting with a 10-gram sample:

• After the first half-life (0.001 s), 5 grams remain.
• After the second half-life (0.002 s), 2.5 grams remain.
• After the third half-life (0.003 s), 1.25 grams remain.

Therefore, after 0.003 seconds, a 10-gram sample of Po-214 would be reduced to 1.25 grams.

Answer 2

You would be left with 1.25 g.

After 0.001 second, 10 grams decays to 5 grams.

After another 0.001 second, 5 g decays to 2.5 g. (Total time 0.002 s; two half-lives have passed)

After another 0.001 second, 2.5 g decays to 1.25 g. (Total time 0.003 s; 3 half-lives have passed)