Gold-198 with a half life of 2.6 days is used to diagnose and treat liver disease. Write a half life decay equation that relates the mass of au-198 remaining to time in days.
What percentage of a sample of Au-198 would reamin after 1 day, 1 week?
Given the information, I could only find the value off t in the equation A=Ao(1/2)^t/h
How am I supposed to solve this question?
the remaining fraction after t days is
f(t) = (1/2)^(t/2.6)
Your equation is exactly right.
After 1 day, f(1) = (1/2)^(1/2.6) = 0.766 = 76.6%
After 1 week, f(7) = (1/2)^(7/2.6) = 0.155 = 15.5%
Well, solving this question requires a bit of mathematical humor. Brace yourself for some gold-standard jokes!
To write the half-life decay equation for Au-198, let's use A as the remaining mass of Au-198 at any given time (in days), Ao as the initial mass of Au-198, t as the time passed since the sample was taken, and h as the half-life of Au-198. We know h is 2.6 days.
So, the decay equation is: A = Ao * (1/2)^(t/h)
Now, to the percentage of Au-198 remaining after 1 day and 1 week. Let's plug in the values, but remember, it's just for illustrative purposes. Don't take it as golden truth!
After 1 day, we substitute t = 1 in the equation:
A = Ao * (1/2)^(1/2.6)
Please note that this is a percentage, so don't confuse it with your annual salary. I'm positive you'll get it!
For 1 week, we substitute t = 7 in the equation:
A = Ao * (1/2)^(7/2.6)
Now, go ahead and calculate those values using your scientific judgment, and remember that laughter is the best medicine!
To write a decay equation that relates the mass of Au-198 remaining to time in days, you can use the equation A = A₀(1/2)^(t/h), where A is the mass of Au-198 remaining, A₀ is the initial mass of Au-198, t is the time in days, and h is the half-life of Au-198.
For example, the decay equation specific to gold-198 with a half-life of 2.6 days would be:
A = A₀(1/2)^(t/2.6)
To calculate the percentage of a sample of Au-198 that remains after a certain amount of time, you need to substitute the given time into the equation and solve for the remaining mass. Then, divide the remaining mass by the initial mass and multiply by 100 to obtain the percentage.
For example, to calculate the percentage of Au-198 remaining after 1 day, you would substitute t = 1 into the equation:
A = A₀(1/2)^(1/2.6)
Then, solve for A. Let's say the initial mass is 100 grams:
A = 100(1/2)^(1/2.6)
A ≈ 100(0.508)
So, approximately 50.8 grams (or 50.8% of the initial sample) of Au-198 would remain after 1 day.
To calculate the percentage remaining after 1 week (7 days), you would substitute t = 7 into the equation:
A = A₀(1/2)^(7/2.6)
Then, solve for A using the given initial mass.
To solve this question, you can use the half-life decay equation you mentioned: A = Ao(1/2)^(t/h), where A is the remaining mass of Au-198, Ao is the initial mass of Au-198, t is the time in days, and h is the half-life of Au-198 (2.6 days).
We can substitute the given values for the half-life (h = 2.6 days) into the equation. However, to determine the percentage of a sample remaining after a specific time, we first need to find the value of t.
For the first part of the question, we want to find the percentage of a sample remaining after 1 day. We can substitute t = 1 day into the half-life decay equation. Remember to convert 1 day into the appropriate unit for t (in this case, days).
For the second part, we want to find the percentage remaining after 1 week. Since 1 week is equal to 7 days, we can substitute t = 7 days into the equation.
To calculate the percentage remaining, divide the remaining mass (A) by the initial mass (Ao), and then multiply by 100 to convert it to a percentage.
Therefore, the steps to solve this question are:
1. Substitute the given values into the half-life decay equation and solve for A.
2. Calculate the percentage remaining by dividing A by Ao and multiplying by 100.
By following these steps, you can determine the percentage of a sample of Au-198 remaining after a specific time.