if a 84g sample of thorium decays with a 10 minute half life, how much would the sample weight in a half hour?
half hour = 30 min = 3 half lives
84 * 1/2 * 1/2 * 1/2 = 84/8 = 10.5g
or in general
mass = original mass /2^n
where n is the number of half lives
To find out how much the sample would weigh in half an hour, we need to determine how many half-lives have passed in that time period.
The half-life of thorium is given as 10 minutes, which means that every 10 minutes, half of the sample decays. Since we are looking at half an hour, we divide 30 minutes by 10 minutes to find out how many half-lives have passed:
30 minutes / 10 minutes = 3 half-lives
Now we can calculate the remaining weight of the sample after three half-lives have passed.
After each half-life, the sample would have lost half of its weight. So, after three half-lives, the weight remaining would be calculated as:
(Initial weight) * (1/2) * (1/2) * (1/2)
The initial weight of the sample is given as 84g, so we can substitute this value into the equation:
84g * (1/2) * (1/2) * (1/2) = 10.5g
Therefore, the sample would weigh 10.5 grams after half an hour.
To determine how much the sample would weigh after half an hour, we need to consider the concept of half-life. The half-life is the time it takes for half of the substance to decay.
In this case, the half-life of thorium is given as 10 minutes. This means that after every 10 minutes, the thorium sample will be reduced to half its original weight.
To solve this problem, we need to find out how many half-lives occur in half an hour (30 minutes).
Since each half-life is 10 minutes, we can calculate the number of half-lives by dividing the total time (30 minutes) by the length of one half-life (10 minutes).
30 minutes ÷ 10 minutes = 3 half-lives
So, after three half-lives (30 minutes), the sample of thorium will have gone through three cycles of halving in weight.
Let's calculate the weight of the sample after each half-life:
- After the first half-life, the sample will weigh half of its initial weight: 84g ÷ 2 = 42g
- After the second half-life, the sample will weigh half of the weight from the previous step: 42g ÷ 2 = 21g
- After the third half-life, the sample will weigh half of the weight from the previous step: 21g ÷ 2 = 10.5g
Therefore, after half an hour (30 minutes), the thorium sample would weigh approximately 10.5 grams.