Strontium-90 is a radioactive waste product from nuclear reactors. It has a half life of 29 years. How many years would it take for a quantity of strontium-90 to decay 1/16 of its original mass?
(1/2)^n = 1/16
n = 4 half lives
4 * 29 = 116 years
if you did not see that 2^4 = 16 then you could do
.5^n = .0625
n log .5 = log .0625
n = log .0625 / log .5
Well, let's do some radioactive math, shall we?
Since strontium-90 has a half-life of 29 years, it means that every 29 years, the amount of strontium-90 will be reduced by half. So, if we want to find out how many times it needs to be halved to reach 1/16 of its original mass, we need to figure out how many half-lives that is.
To do that, we can use the following equation:
(1/2)^n = 1/16
Now, let's solve it together, shall we?
(1/2)^n = (1/2)^4
Since both sides of the equation have the same base (1/2), we can equate the exponents:
n = 4
That means it would take 4 half-lives for a quantity of strontium-90 to decay to 1/16 of its original mass.
So, to find out the number of years it would take, we simply multiply the half-life by the number of half-lives:
29 years x 4 half-lives = 116 years
Hence, it would take approximately 116 years for a quantity of strontium-90 to decay 1/16 of its original mass.
Now, that's some decaying humor for you!
To find the time it takes for a quantity of strontium-90 to decay 1/16 of its original mass, we can use the formula for radioactive decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) is the amount of remaining strontium-90 at time t
N₀ is the original amount of strontium-90
t is the time that has passed
h is the half-life of strontium-90
In this case, we want to find the time it takes for the remaining mass (N(t)) to be 1/16 (1/2^4) of the original mass (N₀). Let's substitute the values:
1/16 = 1/2^4 = N₀ * (1/2)^(t/29)
Now, let's solve for t:
1/16 = (1/2)^(t/29)
2^(-4) = 2^(t/29)
Since the bases are the same, we can equate the exponents:
-4 = t/29
Now, let's solve for t:
t = -4 * 29
t = -116
The negative value indicates that the decay has not occurred yet, so we need to take the absolute value:
t = |-116|
t = 116
Therefore, it would take 116 years for a quantity of strontium-90 to decay 1/16 of its original mass.
To determine the number of years it would take for a quantity of strontium-90 to decay 1/16 of its original mass, we can use the concept of half-life.
The half-life of strontium-90 is given as 29 years, which means that after 29 years, half of the original amount of strontium-90 will have decayed. This implies that the remaining amount will be 1/2 of the original mass.
Since we want to find the time it takes for the mass to decrease to 1/16 (or 1/2^4) of the original mass, we need to determine how many half-lives are required for this reduction.
Let's calculate:
1st half-life: 1/2 of the original mass remains
2nd half-life: 1/4 (1/2 * 1/2) of the original mass remains
3rd half-life: 1/8 (1/2 * 1/2 * 1/2) of the original mass remains
4th half-life: 1/16 (1/2 * 1/2 * 1/2 * 1/2) of the original mass remains
Therefore, it would take 4 half-lives for the quantity of strontium-90 to decay to 1/16 of its original mass.
Since each half-life is 29 years, we can multiply the half-life by the number of half-lives to get the total time:
4 half-lives * 29 years per half-life = 116 years
Thus, it would take 116 years for a quantity of strontium-90 to decay to 1/16 of its original mass.