After how many half-lives does 15/16 of a radioactive sample decay?

After how many half-lives does 15/16 of a radioactive sample decay?

• A. 1 half-life
• B. 2 half-lives
• C. 4 half-lives
• D. 8 half-lives

Answer: (C)

To determine how many half-lives it takes for 15/16 of a radioactive sample to decay, we first need to understand the concept of half-lives. A half-life is the amount of time it takes for half of a radioactive substance to decay. Starting with a sample, let's label the initial amount as 1 (representing the whole sample). - After the first half-life, half of the sample remains, so we have 1/2 remaining. - After the second half-life, half of the remaining 1/2 decays, leaving us with 1/4 left. - After the third half-life, we take half of 1/4, which leaves us with 1/8 remaining. - After the fourth half-life, we take half of 1/8, leading to 1/16 remaining. So, after four half-lives, 1/16 of the sample remains, meaning that 15/16 of the original sample has decayed. This calculation demonstrates why four half-lives must pass for 15/16 of the original sample to decay. Understanding the exponential decay process is crucial in solving such problems, and in this case, it requires recognizing how the fraction

To determine how many half-lives it takes for 15/16 of a radioactive sample to decay, we first need to understand the concept of half-lives. A half-life is the amount of time it takes for half of a radioactive substance to decay.

Starting with a sample, let's label the initial amount as 1 (representing the whole sample).

• After the first half-life, half of the sample remains, so we have 1/2 remaining.

• After the second half-life, half of the remaining 1/2 decays, leaving us with 1/4 left.

• After the third half-life, we take half of 1/4, which leaves us with 1/8 remaining.

• After the fourth half-life, we take half of 1/8, leading to 1/16 remaining.

So, after four half-lives, 1/16 of the sample remains, meaning that 15/16 of the original sample has decayed.

This calculation demonstrates why four half-lives must pass for 15/16 of the original sample to decay. Understanding the exponential decay process is crucial in solving such problems, and in this case, it requires recognizing how the fraction