Solving a Half-Life Physics Problem: Estimating Radon-222 Atom Decay in 12 Days

[mustang]

Radon-222 is a radioactive gas with a half-life of 3.82 days. A gas sample contains 4.5*10^8 radon atoms initially.
Estimate how many radon atoms will remain after 12 days.
This Is what i have done:
3.82 days=3.82*24*60*60=330048seconds
what's next?

 

[Doc Al]

12 days is how many half-lives? What does half-life mean? How much is left after one half-life? Two half-lives?

 

[BobG]

You don't need seconds. After one half-life, you're dividing by 2. If you determine how many half-lifes are in 12 days, you'll know how many times to divide by 2.

As an example, if you divided by 2 twice, you would have:

$$\frac{4.5 \ast 10^8}{2 \ast 2}$$

or

$$\frac{4.5 \ast 10^8}{2^2}$$

If dividing by 2 three times:

$$\frac{4.5 \ast 10^8}{2 \ast 2 \ast 2}$$

or

$$\frac{4.5 \ast 10^8}{2^3}$$

The power in the denominator is however many times you want to divide by 2 and doesn't have to be an integer.