The half-life of P-32 is 14 days. How long after a sample is delivered can a laboratory wait to use a sample in an experiment if they need at least 10 percent of the original radioactivity?
I need help on how to set up this problem. What is the general equation to use for a half-life problem? And a question specific to the problem, is how to I find 10% of the original?
Thanks for your help.
Here's how you do it.
k = 0.693/t1/2
Substitute and solve for k. Substitute k into the below equation.
ln(No/N) = kt
No = atoms you start with.
N = atoms you end with
k from above
t = time.
The easy way to do this problem is to let No = 100 (but you can pick any number you like)
then N = 10 (or 0.1 x the number you picked for No.
Then solve for t.
I did this several years ago with Cu-64 which has a half life of about 13 hours. Since it took almost two days to get to me (by air) and another 12-14 hours to run the experiment, it had to be HOT HOT HOT when it left the manufacturer so it would be at least HOT when I started counting.
ok, so I got 3.32, so would I just multiply that by the half-life? Because the answer choices are 28 days, 14 days, 42 days, 56 days, and 70 days
Just Kidding I got 46.51, but that is not one of the answer choices, so which would I pick? or did I do it wrong?
I obtained 46.5 days, also. So pick 42 days for the answer. That's the closest choice you have. These multiple guess questions OFTEN don't have the exact answer but one close to it.
Ok thanks, yes that answer was right, thanks so much for explaining the equation to me, it makes total sense now!
To solve this problem, you need to understand the concept of half-life and how it relates to the decay of radioactive substances.
The general equation used for a half-life problem is given by:
Remaining Amount = Initial Amount * (1/2)^(t / half-life)
Where:
- Remaining Amount is the amount of the substance left after time t.
- Initial Amount is the original amount of the substance.
- t is the time that has passed.
- Half-life is the time it takes for the substance to decay by half.
Now, let's proceed to set up the problem.
First, you need to find the time after which the laboratory can wait to use the sample. Let's call this time "t".
The lab needs at least 10 percent of the original radioactivity. In other words, the remaining amount of the substance should be equal to or greater than 10% of the initial amount.
To convert this to an equation, you can say that:
Remaining Amount >= 0.1 * Initial Amount
Next, substitute the general equation for remaining amount in terms of the initial amount and the half-life:
Initial Amount * (1/2)^(t / half-life) >= 0.1 * Initial Amount
Simplify the equation by canceling out the Initial Amount from both sides:
(1/2)^(t / half-life) >= 0.1
Now, you need to solve for "t". To do that, you can take the logarithm (base 1/2) of both sides of the equation:
log(base 1/2) (1/2)^(t / half-life) >= log(base 1/2) 0.1
Using the properties of logarithms, the equation simplifies to:
t / half-life >= log(base 1/2) 0.1
Finally, multiply both sides of the inequality by the half-life to isolate "t":
t >= half-life * log(base 1/2) 0.1
To find the value of log(base 1/2) 0.1, divide the logarithm of 0.1 with base 1/2 by the logarithm of 1/2 with base 1/2:
t >= half-life * (log(base 1/2) 0.1 / log(base 1/2) 1/2)
Since log(base 1/2) 1/2 is equal to 1, the equation simplifies to:
t >= half-life * (log(base 1/2) 0.1)
Now, you have the equation set up to solve for "t". Plug in the given half-life of P-32 (14 days) into the equation, and calculate log(base 1/2) 0.1 using a calculator. This will give you the minimum time the lab can wait before using the sample in the experiment.