A sample of a material has 2000 radioactive particles in it today. Your grandfather measured 4000 radioactive particles in it 60 years ago.?

Since the half-life (the amount of time it takes for a radioactive material to have half it's mass) of the material is 60 years, every 60 years, the amount of radioactive particles is cut in half. 60 years from now, the mass will be half of what it is today, so:

2000 / 2 = 1000 radioactive particles.

This is the same for 120 years, except 2 intervals have passed. In 60 years, it will have 1000 particles, so in another 60 years, it will cut in half again:

1000 / 2 = 500 radioactive particles.

To summarize, in 60 years, there will be 1000 radioactive particles, and in 120 years, there will be 500 radioactive particles.

Looks like every 60 years it reduces by a half...life