if carbon 14 has a half life of 24 days how much would be left of 220 gram sample after 168 days
the amount left after t days is
220 (1/2)^(t/24)
so,
220(1/2)^(168/24) = 1.718g
168 days is 7 half-lives, so 1/128 remains.
To determine how much would be left of a 220 gram sample of carbon-14 after 168 days, we can use the formula for exponential decay:
N = N₀ * (1/2)^(t / t₁/₂)
where:
- N is the amount of sample remaining after time t
- N₀ is the initial amount of the sample
- t is the elapsed time
- t₁/₂ is the half-life of the substance
In this case, N₀ = 220 grams, t = 168 days, and t₁/₂ = 24 days.
Plugging these values into the formula, we get:
N = 220 * (1/2)^(168 / 24)
Now, let's calculate the value:
N = 220 * (1/2)^(7)
To evaluate (1/2)^7, we can simplify the fraction:
(1/2)^7 = (1^7) / (2^7) = 1/128
Now, let's substitute this value back into the equation:
N = 220 * (1/128) = 1.71875 grams
Therefore, after 168 days, there would be approximately 1.71875 grams of the carbon-14 sample remaining.