Question

You have 400 kg of a radioactive substance with a short half-life of 1000 years. how much will be left after these times?

Answer 1

Half-life of a radioactive substance is the time required to reduce the amount of substance to half of its initial amount. 

In present case, half-life is material is given as 1000 years and initial amount of material is given as 400 kg
 
Answer 1) Since, half-life of radio-active substance is 1000 years, therefore after 1st half life, amount of the material will be left to half the initial amount. Hence, amount of substance left after 1000 years = 400/2 = 200 kg.

Answer 2) For 2000 years, radioactive material has crossed 2 times the half life. Therefore ,  amount of the material will be left to 1/4 the initial amount. Hence, amount of substance left after 2000 years = 400/4 = 100 kg.

Answer 3)  For 4000 years, radioactive material has crossed 4 times the half life. Therefore , amount of the material will be left to 1/16 the initial amount. Hence, amount of substance left after 4000 years = 400/16 = 25 kg.