A sample of a material has 200 radioactive particles in it today. Your grandfather measured 400 radioactive particles in it 90 years ago.

a) 90 years from today, how many radioactive particles will the sample have?

b) 180 years from today, how many radioactive particles will the sample have?

Half life is the time at which the concentration of the reactant reduced to half. So, according to the given question, the particles decayed from 400 particles to 200 particles in 90 years.

It means that the half life of the decay is 90 years.

(a) 90 years from now, means that another half life is achieved means, 200 will reduced to half on decay.

Thus, The sample will have 100 radioactive particles.

(a) 180 years from now, means that 2 half lives is achieved means, 200 will reduced to half and then again half on decay.

Thus, The sample will have 50 radioactive particles.