Strontium-90 has half-life of 28 years. if a 1.00-mg sample was stored for 112 years. what mass of Sr-90 would remain?
To find the mass of Sr-90 that would remain after 112 years, we can use the formula for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
Where:
N(t) = the remaining amount of Sr-90 after time t
N₀ = the initial amount of Sr-90 (1.00 mg in this case)
t = time that has passed (112 years in this case)
h = half-life of Sr-90 (28 years in this case)
Let's calculate it now step-by-step:
1. Find the number of half-lives that have occurred:
number of half-lives = t / h
number of half-lives = 112 years / 28 years = 4
2. Calculate the remaining amount using the formula for exponential decay:
N(t) = N₀ * (1/2)^(t/h)
N(t) = 1.00 mg * (1/2)^(4)
N(t) = 1.00 mg * (1/2)^4
N(t) = 1.00 mg * (1/16)
N(t) = 0.0625 mg
Therefore, the mass of Sr-90 that would remain after 112 years is 0.0625 mg.
To determine the mass of Sr-90 that would remain after 112 years, we can use the concept of half-life. The half-life of a radioactive substance is the time it takes for half of the sample to decay.
Given that the half-life of Sr-90 is 28 years, we can calculate the number of half-lives that have passed in 112 years:
Number of half-lives = time passed / half-life
Number of half-lives = 112 years / 28 years = 4 half-lives
Since each half-life reduces the amount of Sr-90 by half, after four half-lives, we only have 1/2^4 = 1/16 of the original amount remaining. Therefore, the mass of Sr-90 that would remain after 112 years is:
Mass remaining = original mass * (1/2)^number of half-lives
Mass remaining = 1.00 mg * (1/2)^4
Mass remaining = 1.00 mg * (1/16)
Mass remaining = 0.0625 mg
So, after 112 years, approximately 0.0625 mg of Sr-90 would remain.
k = 0.693/t1/2
Substitute k in the following:
ln(No/N) = kt
No = 1 mg
N = mg remaining after t time
k from above.
t = 112 years.