Final answer:
It will take approximately 2.622 x 10^9 years for 875 g of uranium-238 to decay to thorium-234.
Step-by-step explanation:
Uranium-238 decays into thorium-234 by emitting an alpha particle. The half-life of uranium-238 is 4.5 × 10^9 years.
To find out how long it will take for 875 g of uranium-238 to decay, we need to use the decay law formula:
N(t) = N(0) × (1/2)^(t / T1/2)
Where N(t) is the amount of radioactive material at time t, N(0) is the initial amount of radioactive material, t is the time elapsed, and T1/2 is the half-life.
Plugging in the values, we have:
875 g = 1000 g × (1/2)^(t / 4.5 × 10^9)
Rearranging the equation and solving for t, we get:
t = (4.5 × 10^9) × log2(875/1000)
Using a calculator, we find that t is approximately 2.622 x 10^9 years.