If the sample has a half life of 5 seconds, how much is left after 25 seconds?
12.5%
25%
3.125%**
6.25%
25 s is 5 half-lives
(1/2)^5 = 1/32
looks correct
To calculate the amount left after a certain time, we can use the formula for exponential decay:
Amount remaining = (Initial amount) * (1/2)^(time / half-life)
In this case, the half-life is given as 5 seconds. So, after 5 seconds, half of the initial amount will remain.
Let's plug in the given values:
Amount remaining = (Initial amount) * (1/2)^(25 / 5)
Simplifying, we get:
Amount remaining = (Initial amount) * (1/2)^5
Now, we can calculate the amount remaining:
Amount remaining = (Initial amount) * (1/2)^5
Since the initial amount is not given, we cannot determine the exact amount remaining. However, we can determine the percentage of the initial amount remaining.
Let's calculate the percentage:
Percentage remaining = Amount remaining / Initial amount * 100%
Percentage remaining = [(Initial amount) * (1/2)^5] / (Initial amount) * 100%
The initial amount cancels out:
Percentage remaining = (1/2)^5 * 100%
Simplifying further:
Percentage remaining = (1/2)^(5) * 100%
Percentage remaining = 1/32 * 100%
Finally, we can calculate the exact percentage:
Percentage remaining = 3.125%
Therefore, the correct answer is 3.125%, as indicated by the option "3.125%" in the available choices.
The other choice was
1.5625%