Question
Refer to the line graph below to answer Q7 and Q8.
Q7.
a) After three (3) half-lives, x parent isotope should have decayed by how many years? (1mk)
b) How many milligrams of a 6.5×10-2kg sample of the x parent isotope will remain at the end of
(a)? (3mks)
Q7.
a) After three (3) half-lives, x parent isotope should have decayed by how many years? (1mk)
b) How many milligrams of a 6.5×10-2kg sample of the x parent isotope will remain at the end of
(a)? (3mks)
Answers
GPT-4o mini
To answer your questions regarding the x parent isotope after three half-lives, we need some information about the half-life of the isotope, which is typically represented on the line graph that you referred to. Since I can't see the graph, I'll provide you with a general methodology for how you can calculate the answers once you have that information.
### Q7
**a)** To determine how many years x parent isotope will have decayed after three half-lives, you can use the formula:
\[
\text{Total time} = 3 \times \text{Half-life}
\]
So you need to look at the half-life of the isotope on your graph. Multiply that by three to get the total time in years.
**b)** To find out how much of the parent isotope remains after three half-lives, you can use the formula for exponential decay based on half-lives:
\[
\text{Remaining amount} = \text{Initial amount} \times \left( \frac{1}{2} \right)^{n}
\]
Where \( n \) is the number of half-lives.
For a \( 6.5 \times 10^{-2} \, \text{kg} \) sample:
1. Convert kg to mg (since there are \( 1,000 \, \text{mg} \) in \( 1 \, \text{g} \) and \( 1000 \, \text{g} \) in \( 1 \, \text{kg} \)):
\[
6.5 \times 10^{-2} \, \text{kg} = 65 \, \text{g} = 65000 \, \text{mg}
\]
2. Substituting the values into the remaining amount formula:
\[
\text{Remaining amount} = 65000 \times \left( \frac{1}{2} \right)^{3} = 65000 \times \frac{1}{8}
\]
\[
= 8125 \, \text{mg}
\]
Thus, at the end of part **(a)**, you would determine the years based on the half-life, and for part **(b)** the remaining amount of the isotope would be 8125 mg after three half-lives.
If you are able to provide me with specific values from your graph, I can help you calculate the exact answers.
### Q7
**a)** To determine how many years x parent isotope will have decayed after three half-lives, you can use the formula:
\[
\text{Total time} = 3 \times \text{Half-life}
\]
So you need to look at the half-life of the isotope on your graph. Multiply that by three to get the total time in years.
**b)** To find out how much of the parent isotope remains after three half-lives, you can use the formula for exponential decay based on half-lives:
\[
\text{Remaining amount} = \text{Initial amount} \times \left( \frac{1}{2} \right)^{n}
\]
Where \( n \) is the number of half-lives.
For a \( 6.5 \times 10^{-2} \, \text{kg} \) sample:
1. Convert kg to mg (since there are \( 1,000 \, \text{mg} \) in \( 1 \, \text{g} \) and \( 1000 \, \text{g} \) in \( 1 \, \text{kg} \)):
\[
6.5 \times 10^{-2} \, \text{kg} = 65 \, \text{g} = 65000 \, \text{mg}
\]
2. Substituting the values into the remaining amount formula:
\[
\text{Remaining amount} = 65000 \times \left( \frac{1}{2} \right)^{3} = 65000 \times \frac{1}{8}
\]
\[
= 8125 \, \text{mg}
\]
Thus, at the end of part **(a)**, you would determine the years based on the half-life, and for part **(b)** the remaining amount of the isotope would be 8125 mg after three half-lives.
If you are able to provide me with specific values from your graph, I can help you calculate the exact answers.