A quantity of oxygen gas had 16.32 g of the radioactive isotope oxygen-19 in it. When measured exactly 10 minutes later, the amount of oxygen-19 was 0.964 g. What is the half-life, in seconds, of oxygen-19?

16.32(1/2)^(t/k) = .964 , where t is in minutes, and k is the half-life in minutes.

(.5)^(10/k) = .0590686.. ( I stored it)
ln both sides

(10/k) ln .5= ln (.059068...)
10/k = 4.081464...
k = 2.4504 minutes or 147.006 seconds

To find the half-life of oxygen-19, we need to calculate the time it takes for half of the initial amount of oxygen-19 to decay.

We know that the initial quantity of oxygen-19 is 16.32 g, and after 10 minutes, it becomes 0.964 g.

To find the half-life, we can use the formula:

amount = initial amount * (1/2)^(time / half-life)

Rearranging the formula to solve for half-life, we have:

half-life = time / log(base 1/2) (amount / initial amount)

Substituting the given values into the formula:

half-life = 10 minutes / log(base 1/2) (0.964 g / 16.32 g)

Now we will convert the time to seconds since the half-life is required in seconds:

half-life = 10 minutes * 60 seconds / log(base 1/2) (0.964 g / 16.32 g)

To evaluate the logarithm, we need to convert the fraction into a decimal:

half-life = 10 minutes * 60 seconds / log(0.0589)

Using a calculator to find the logarithm:

half-life ≈ 1800 seconds / (-2.83027)

Evaluating the expression:

half-life ≈ -637.06 seconds

Since time cannot be negative, we disregard the negative sign:

half-life ≈ 637.06 seconds

Therefore, the half-life of oxygen-19 is approximately 637.06 seconds.