Suppose a laboratory has a 26 g sample of polonium-210. The half-life of polonium-210 is about 138 days.?
To find out how much polonium-210 remains after a certain amount of time, we will use the concept of half-life.
The formula for calculating the remaining amount of a substance after a given number of half-lives is:
N = N₀ × (1/2)^(t / t₁/₂)
Where:
N is the remaining amount of polonium-210,
N₀ is the initial amount of polonium-210,
t is the time elapsed in days,
t₁/₂ is the half-life of polonium-210.
Let's plug in the values:
N₀ = 26 g
t₁/₂ = 138 days
Now, let's assume we want to calculate the amount of polonium-210 remaining after 276 days (2 half-lives).
First half-life (138 days):
N = 26 g × (1/2)^(138 / 138)
N = 26 g × (1/2)^1
N = 26 g × 0.5
N = 13 g
Second half-life (276 days):
N = 13 g × (1/2)^(276 / 138)
N = 13 g × (1/2)^2
N = 13 g × 0.25
N = 3.25 g
Therefore, after 276 days, there would be approximately 3.25 g of polonium-210 remaining in the laboratory sample.