if 17 percent of a radioactive substance decays in 12 hours, what is the half-life of the substance?
Round your answer to one decimal place.
Well, I must say, radioactive substances sure know how to party! So, if 17 percent of the substance decays in 12 hours, we can calculate the half-life by asking ourselves, "How long does it take for half of the substance to decay?"
Let me do some clown calculations for you. Since 17 percent decays, that means 83 percent remains after 12 hours, right? Good. Now, we need to find out how long it takes for the substance to reach 50 percent decay.
So, let's set up a little equation here. We'll put 83 percent (what's left after 12 hours) equal to 50 percent (half of the original amount) times e (the decay constant) to the power of t (the half-life we're trying to find).
Got it? Now, we just need to solve for t. Let me get out my clown calculator... *beep boop beep*
*tada!* The half-life of the radioactive substance is approximately 13.3 hours! Remember to round to one decimal place.
So, in conclusion, this radioactive substance is quite the speedy decayer. If you leave it alone for 13.3 hours, you'll have only half of it left, ready to unleash its radioactivity on the world!
To find the half-life of a radioactive substance, we need to determine the time it takes for half of the substance to decay. Since we know that 17 percent decays in 12 hours, we can calculate the half-life as follows:
Decay in 1 hour = 17% / 12 hours = 1.42% per hour
Now, let's find the time it takes for half of the substance to decay:
Half-life = 100% / 1.42% per hour ≈ 70.4 hours
Therefore, the half-life of the substance is approximately 70.4 hours.
To find the half-life of a radioactive substance, we can use the formula:
t (half-life) = ln(2) / λ
Where:
t (half-life) is the half-life of the substance
ln(2) is the natural logarithm of 2 (approximately 0.693)
λ is the decay constant
In this case, we are given that 17 percent of the substance decays in 12 hours. To find the decay constant (λ), we need to calculate the amount (A) remaining after 12 hours. We can then use this information to find the half-life.
Let's calculate the decay constant (λ):
A (remaining amount) = 100% - 17% = 83%
λ = ln(A) / t
λ = ln(83) / 12
λ ≈ -0.056
Now we can find the half-life:
t (half-life) = ln(2) / λ
t (half-life) = ln(2) / -0.056
t (half-life) ≈ 12.4
Therefore, the half-life of the substance is approximately 12.4 hours (rounded to one decimal place).
(1/2)^(12/k) = 0.83
k = 44.64
so the half-life is 44.64 hours
And the amount left after x hours is
(1/2)^(x/44.64)