element x has a half life of 90 seconds. How much of a 100 gram sample of element x is left after half an hour
To determine how much of a sample is left after a certain period of time, we can use the concept of half-life. The half-life is the amount of time it takes for half of the substance to decay.
In this case, the half-life of element X is given as 90 seconds. To find out how much remains after half an hour (30 minutes or 1800 seconds), we need to determine how many half-lives have passed during this time.
The formula to calculate the number of half-lives is:
Number of half-lives = elapsed time / half-life
Plugging in the values:
Number of half-lives = 1800 seconds / 90 seconds = 20 half-lives
Now, we can calculate the remaining amount of element X using the formula:
Remaining amount = initial amount * (1/2)^(number of half-lives)
Plugging in the values:
Remaining amount = 100 grams * (1/2)^(20 half-lives)
Using a calculator, we can compute the result:
Remaining amount = 100 grams * 0.000000953...
Approximately, the remaining amount of element X after half an hour is:
Remaining amount ≈ 0.0000953 grams
Therefore, after half an hour, there would be approximately 0.0000953 grams of element X left from a 100 gram sample.