The iodine-131 nuclide has a half-life of 8.0 days. If you originally have a 257 g sample, after 48 days how much will you have?
1 half life is 8 days.
48 days / 8 days per half life = 6 half lives that occur, so we halve our original amount 6 times.
Amount remaining = 257 g * (1/2)^6
Well, let me dig up my trusty clown calculator to help with this radioactive math problem!
Now, the half-life of iodine-131 is 8.0 days. This means that every 8 days, half of the iodine-131 will decay. So after 48 days, we need to figure out how many half-lives have passed.
48 days divided by 8 days per half-life gives us 6 half-lives.
Now, after each half-life, the amount of iodine-131 remaining is reduced by half. So if we start with 257 grams, after one half-life we'll have 128.5 grams, after two half-lives we'll have 64.25 grams, and so on.
Calculating it for each half-life, we have:
257 g -> 128.5 g -> 64.25 g -> 32.125 g -> 16.0625 g -> 8.03125 g -> 4.015625 g
So, after 48 days, you would have approximately 4.02 grams of iodine-131 left. But hey, don't be too sad about the decay, it's just iodine going through a rebellious phase!
To find the amount of iodine-131 remaining after 48 days, we can use the formula:
Amount remaining = Initial amount * (1/2)^(Number of half-lives)
First, let's calculate the number of half-lives that occur in 48 days:
Number of half-lives = 48 days / 8.0 days per half-life
Number of half-lives = 6
Now, we can plug in the values into the formula:
Amount remaining = 257 g * (1/2)^6
Amount remaining = 257 g * (1/64)
Amount remaining = 4.0156 g
Therefore, after 48 days you would have approximately 4.0156 grams of iodine-131 remaining.
To determine the amount of iodine-131 remaining after 48 days, we can use the half-life formula.
The formula for calculating the remaining amount of a substance after a given time is:
A = A₀ * (1/2)^(t / T₁/₂)
Where:
A = Final amount of the substance
A₀ = Initial amount of the substance
t = Time that has passed
T₁/₂ = Half-life of the substance
In this case, the initial amount (A₀) of iodine-131 is 257 g, the time (t) is 48 days, and the half-life (T₁/₂) is 8.0 days.
Let's substitute these values into the formula:
A = 257 g * (1/2)^(48 / 8)
To simplify the calculation, let's start by calculating (1/2)^(48 / 8):
(1/2)^(48 / 8) = (1/2)^6 = 1/64
Now, we can substitute this value back into the formula:
A = 257 g * 1/64
To calculate the final amount (A), we need to multiply 257 g by 1/64:
A = 4.015625 g
Therefore, after 48 days, you will have approximately 4.02 g of iodine-131 remaining.