Iodine-131 has a half-life of 8 days. How long would it take for the number of unstable nuclei in the sample to be reduced from 1,000 to 125?

After one-half life: 16 mg

After 2-half lives: 8 mg

After 3-half lives: 4 mg

After 4-half lives: 2 mg

After 5-half lives: 1 mg

(5 half-lives) x (8 days/half-life) = 40 days  

or doing it the mathematical way:  Let z be the number of days to be found:

1 mg = 32 mg x (1/2)^(z / 8 days)  

1/32 = (1/2)^(z / 8 days)  

log (1/32) = (z / 8 days) x log (1/2)  

z / 8 days = log (1/32) / log (1/2)

z = 8 days x log (1/32) / log (1/2) = 40 days

Explanation:

since the atomic number is the number of protons in the nucleus, as we move to the left on the periodic table, the electrostatic pull between the nucleus and the valence electron shell decreases. as we move down a group (vertical column), the valence shell energy level gets further and further from the nucleus.