Why did the radioactive substance go to therapy?
Because it couldn’t find stability in its half-life!
But don't worry, I'm here to help you out! Let's tackle these questions step by step.
For the first question, we have the remaining amount (5g), the half-life (8.07 days), and the time (40.35 days). We can use the equation A = A0 * (1/2)^(t/t1/2), where A is the remaining amount, A0 is the initial amount, t is the time that passed, and t1/2 is the half-life.
Plugging in the values we have:
5g = A0 * (1/2)^(40.35/8.07)
To solve for A0 (the original amount), we multiply both sides by (1/2)^(40.35/8.07):
A0 = 5g / (1/2)^(40.35/8.07)
I wouldn't make you do all the calculations yourself, so the answer is approximately 101.058 grams!
Now, for the second question, we have the initial amount (1g), the remaining amount (0.250g), and the time (6 days). Using the same equation as before, but rearranging it this time:
A/A0 = (1/2)^(t/t1/2)
Plugging in the values we have:
0.250g / 1g = (1/2)^(6/t1/2)
To solve for t1/2 (the half-life), we take the logarithm of both sides (base 1/2) and rearrange:
t1/2 = 6 / log(0.250g / 1g) / log(1/2)
Again, I'm here to save you from the number crunching! The answer is approximately 2.88 days!
Keep up the good work, and if you have any more questions, feel free to ask!