The half life of iodine 131 is 8.02 days how long will it take for 80% of the sample to decay

Half life is the time taken for half of the mass of a sample to disappear,

Given that

 iodine has a half life t_1/2 = 8.02 days.

 let us observe it in this way, after one half-life elapse 50% percent of its mass is given off, and 50% of the mass is left . After another half-life,  ½ of the remaining 50 percent is also gone , we are left with only 25 percent of the original mass.

After two half-life 75% mass is lost. Therefore after another half-life ½ of the remaining 25% which is 12.5% percent of the original mass is left.

Therefore 75% + 12% =87% , therefore after 3 half-lives about 80% is lost

Each half takes 8.02 days

 there 3 * 8.02 = 24.06days

 in a tabular form we can have

S/n	Number of half-life	Amount remaining	Amount decayed	Total	Number of days
1	One	50%	50%	100%	8.02 days
2	Two	25%	75%	100%	14.04 days
3	Three	12.5%	87.5%	100%	24.06 days

Summary after 3 half-lives 87% decayed and  it takes 24.06 days.

There are many isotopes of iodine , they are about 37 in number each having different halflives but all the half-lifes are less than 60 days. The only stable iodine sample is iodine-127. Isotopes iodine-135 has a half-life of less than  seven hours , mening it mass is lost by half every seven days.  The isotopes with the longest halflife is iodine-129 with halflife of 15.7 million years