How many years will it take for 88g tritium to decay to an 11g sample?
k = 0.693/t1/2
Look up the value of half-life in your text or notes (or tables on the Internet).
Then ln(No/N) = kt
No = 88 g
N = 11 g
k = from above.
Solve for t.
Solve for t.
To determine how many years it will take for 88g of tritium to decay to an 11g sample, we need to understand the concept of radioactivity and the half-life of tritium.
Tritium is a radioactive isotope of hydrogen with a half-life of about 12.3 years. The half-life of a radioactive substance is the time it takes for half of the initial amount to decay. In this case, after each 12.3-year period, half of the tritium will have decayed.
To calculate the number of half-lives required for the decay, we can use the formula:
Number of half-lives = (log(final amount / initial amount)) / log(0.5)
Let's calculate:
Number of half-lives = (log(11g / 88g)) / log(0.5)
= (log(0.125)) / log(0.5)
≈ (-0.9031) / (-0.3010)
≈ 3
So, it will take approximately 3 half-lives for 88g of tritium to decay to an 11g sample.
Since each half-life is approximately 12.3 years, we can multiply the number of half-lives by the duration of a single half-life to get the total time:
Total time = Number of half-lives × Half-life duration
= 3 × 12.3 years
≈ 36.9 years.
Therefore, it will take approximately 36.9 years for 88g of tritium to decay to an 11g sample.