The half - life of radium-224 is 3.5 days .what fraction of the sample remain undecaye after fourteen days
We can use the formula for half-life to calculate the fraction of a sample that remains after a certain amount of time:
fraction remaining = (1/2)^(time/half-life)
In this case, the time is 14 days and the half-life is 3.5 days, so we can plug in and simplify:
fraction remaining = (1/2)^(14/3.5)
fraction remaining = (1/2)^4
fraction remaining = 1/16
Therefore, after 14 days, only 1/16th or 0.0625 of the original sample of radium-224 remains undecayed.
To determine the fraction of the sample that remains undecayed after fourteen days, we need to calculate how many half-lives have passed during that time.
Given that the half-life of radium-224 is 3.5 days, we can divide the elapsed time (14 days) by the half-life:
14 days / 3.5 days = 4
This means that four half-lives have passed in this time period.
To find the fraction that remains undecayed after four half-lives, we can use the formula:
Fraction remaining = (1/2)^(number of half-lives)
So, plugging in the number of half-lives into the formula:
Fraction remaining = (1/2)^4
Calculating the fraction:
Fraction remaining = 1/16
Therefore, after fourteen days, only 1/16 of the original sample remains undecayed.