If the radiicativr decay of nuclear explosion contains 90 Sr , with a half life of 28.1 years how long will it take for 99 of this radioaioot to decay
99 what? 99 grams? 99 tons? 99%. I suspect 99%.
Two steps. First determine k.
k = 0.693/t1/2 and substitute into the following:
ln(No/N) = kt
I would set No = 100 if that is 99%.
Then N = 1% (if 99% is gone)
k from above
Solve for t in years.
Sorry don't understand it is 99 percent
Ln(100)/1)=(0.693/t^1/2)(t). ??? Don't get it
There isn't anything to get. Can you punch the calculator? That's all there is to it. Do it in steps. Don't try to muddle it up by putting all of it together.
ln 100/1 = 4.605
0.693/28.1 = 0.02466 = k
so
ln(100/1) = 0.02466*t
4.605 = 0.02466t
and t = 4.605/0.02466 = ? or about 200 years more or less.
To find the time it takes for 99% of the radioactive material to decay, we can use the concept of half-life.
Given that the half-life of 90Sr is 28.1 years, it means that after 28.1 years, half the amount of 90Sr will remain. Continuing this pattern, after another 28.1 years, half of the remaining amount will decay, leaving 25% of the initial amount (50% of 50%).
To determine how long it takes for 99% decay, we can set up the following equation:
Initial amount * (1/2)^(n) = Remaining amount
Where n represents the number of half-lives.
To solve for n, we can rearrange the equation:
(1/2)^(n) = Remaining amount / Initial amount
We know that 99% of the radioactive material decays, so the remaining amount is 1% of the initial amount, or 0.01 times the initial amount:
(1/2)^(n) = 0.01
To find n, we can take the logarithm (base 2) of both sides of the equation:
log2((1/2)^(n)) = log2(0.01)
n * log2(1/2) = -2
Since log2(1/2) is -1, we can simplify further:
n * (-1) = -2
n = 2
Therefore, it takes 2 half-lives for 99% of the radioactive material to decay. Since each half-life is 28.1 years, the total time it takes is:
Total time = Number of half-lives * half-life duration
= 2 * 28.1 years
= 56.2 years
So, it will take approximately 56.2 years for 99% of the 90Sr radioactive material to decay.