calculate the number of days it will take for the mass to be reduced to 3.00μg.

Question

The half-life of radioactive chromium-51 is 28 days. If a sample of chromium -51 has a mass of 12.0 μg, calculate the number of days it will take for the mass to be reduced to 3.00μg.

time: ?days

Answer 1

Radioactive decay is a first order reaction.

For a 1st order reaction a relatively easy formula to us is

FR = 0.5ⁿ

FR = fraction remaining = 3.00 g / 12.0 ug = 0.25

NOTE: This is relatively easy and we don't need a formula or equation. We can do it as follows:

After 1 half life 0.5 is left

After 2 half lives 0.25 is left

So, it will take 2 half lives. 2 half lives x 28 days / half life = 56 days.

If it were more complex, the above formula would be used as follows:

FR = 0.25

n = number of half lives elapsed = ?

0.25 = 0.5ⁿ

log 0.25 = n log 0.5

-0.60 = -0.301 n

n = 2 half lives

2 half lives x 28 days / half life = 56 days