Leutium-176 Decay Calculation

How much leutium-176 will remain after 1.155 x 10^11 years?

Options: 1. 2.10 g 2. 3.00 g 3. 5.56 g 4. 8.40 g

Answer:

The amount left of leutium-176 will be 2.10 g.

In order to calculate the amount of leutium-176 that will remain after 1.155 x 10^11 years, we first need to determine the rate constant. The rate constant can be calculated using the formula: [k = 0.693 / t_(1/2)] [k = 0.693 / 3.85 x 10^10 years] [k = 0.18 x 10^-10 years^-1] Next, we use the rate law for first order kinetics to calculate the amount left of the sample. The formula for the rate law is: [t = 2.303 / k log(a / (a - x))] where: k = rate constant = 0.18 x 10^-10 years^-1 t = decay time = 1.155 x 10^11 years a = initial amount of the sample = 16.8 g a - x = amount left after decay process = ? By substituting the given values into the equation, we can solve for the amount left after decay: 1.155 x 10^11 years = 2.303 / 0.18 x 10^-10 years^-1 log(16.8 / (a - x)) a - x = 2.10 g Therefore, the amount left of leutium-176 after 1.155 x 10^11 years will be 2.10 g.