an original sample of K-40 has a mass of 25.00 grams. After 3.9x 10 to the ninth years, 3.125 grams of the original sample remains unchanged. What is the half-life ok K-40 in minutes?
Is it 6.8328 x 10 to the 14th
Yes but you are allowed only 2 significant figures so you should round to 6.8E14 min.
To find the half-life of K-40 in minutes, we need to use the given information. The half-life of a radioactive substance is the time it takes for half of the original sample to decay.
First, let's determine the fraction of the original sample remaining after 3.9x10^9 years. We can do this by dividing the remaining mass (3.125 grams) by the original mass (25.00 grams):
Fraction remaining = (3.125 grams) / (25.00 grams) = 0.125
Next, we need to determine the number of half-lives that have occurred in 3.9x10^9 years. We can calculate this by taking the logarithm (base 2) of the fraction remaining:
Number of half-lives = log2(0.125) ≈ -3.0
Since a negative number of half-lives doesn't make sense, we need to take the absolute value:
Number of half-lives = 3
Now, we can find the duration of one half-life by dividing the total time (in minutes) by the number of half-lives:
Total time = 3.9x10^9 years = (3.9x10^9 years) * (365 days/year) * (24 hours/day) * (60 minutes/hour) = 6.1784x10^17 minutes
Half-life = Total time / Number of half-lives = (6.1784x10^17 minutes) / 3 ≈ 2.0595x10^17 minutes
Therefore, the half-life of K-40 is approximately 2.0595x10^17 minutes. Note that this value may be rounded to the appropriate number of significant figures.