With a half-life of 14.3 years, how long will it take for100 g of phosphorus32 to decay to 12.5 mg?

To answer this question, we can use the concept of radioactive decay and the formula for exponential decay. The formula for radioactive decay is given by:

N(t) = N0 * (1/2)^(t / T)

Where:
N(t) = the amount of the radioactive substance at time t
N0 = the initial amount of the radioactive substance
t = time elapsed
T = half-life of the radioactive substance

In this case, we are given the initial amount (N0 = 100 g), the final amount (N(t) = 12.5 mg), and the half-life (T = 14.3 years). However, we need to convert the units to be consistent.

1 g = 1000 mg

So, 12.5 mg is equivalent to 12.5 / 1000 = 0.0125 g.

Now, let's rearrange the radioactive decay formula to solve for t:

t = T * log2(N(t) / N0)

Plugging in the values we have:

t = 14.3 * log2(0.0125 / 100)

Using a scientific calculator or an online calculator, we can solve this equation to get the value of t. Plugging in the values into an online calculator, we find:

t ≈ 91.36 years

Therefore, it will take approximately 91.36 years for 100 g of phosphorus-32 to decay to 12.5 mg.