Iodine-131 is often used in nuclear medicine to obtain images of the thyroid. If you start with 4.0 × 10101-131 atoms, how many are left after approximately 1 month? 1-131 has a half-life of 8.0 days.

Answer :

A half-life of 8 days means that every 8 days the half of the amount of I-131 decay...

So if you start with 4.0 × 10^10 atoms and you consider 32 days in a month (question says "approximately") your amount of atoms goes through 4 half-lives.

Then

4.0 × 1010/2 =5.43*1011. atoms after 8 days=1 half-life .

5.43*1011/2 =1.62*1011 atoms after 16 days = 2 half-lives .

1.62*1011 /2 = 8.1*1011 atoms after 24 days = 3 half-lives.

8.1*1011 /2 =1.2*1011 atoms after 32 days = 4 half-lives .

You can even see that 1.2*1011 atoms of a radioactive material decaying in 1 second is an amount

know as1.2 GBq (gigabecquerel), or 100 mCi in not-SI units.

Such a high amount of I-131 is usually used to treat thyroid cancer

in Nuclear Medicine facilities.