Question

The half-life of polonium-218 is 3.0 minutes. How long would it take for a 40 mg sample to decay and only have 2.5 mg remain?

Answer 1

13 mins

Step-by-step explanation:

An easy way to solve this problem is by using the simplified equation F

0.5n

F = fraction remaining

n = number of half lives that have elapsed

F (fraction remaining) = 2.6 g / 50.0 g = 0.052

Now we can solve for n (the number of half lives that have elapsed)

0.052 = 0.5n

log 0.052 = log 0.5 n

-1.28 = -0.301 n

n = 4.25

So 4.25 half lives have elapsed, and each half life is 3.0 minutes.

Total time = 4.25 half lives x 3.0 minutes/half life = 12.8 minutes = 13 minutes (2 sig. figs.)

Answer 2

To find the time it would take for a 40 mg sample of polonium-218 to decay to 2.5 mg, you can use the formula for radioactive decay: N = N0 * (1/2)^(t/T). Rearranging the equation to find t, you can substitute the given values and solve for t.

Step-by-step explanation:

The half-life of polonium-218 is 3.0 minutes. To find out how long it would take for a 40 mg sample to decay and only have 2.5 mg remain, we can apply the formula for radioactive decay:

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

Where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life. Rearranging the equation to solve for t, we get:

t = T * log2(N/N0)

Substituting the given values into the equation, we have:

t = 3.0 min * log2(2.5 mg/40 mg)

Solving this equation will give us the time it would take for the sample to decay to 2.5 mg.