Two different radioactive isotopes decay to 10% of their respective original amounts. isotope a does this in 33 days, while isotope b does this in 43 days. what is the approximate difference in the half-lives of the isotopes? 3 days 10 days 13 days 33 days

3 days  

Explanation:

For each isotope, we must use the integrated rate law for a first order reaction to get the rate constant k, then use that to calculate the half-life t_½.

1. Isotope A

The integrated rate law for a first-order decay is  

ln(N₀/N) = kt

Data:

N₀ = 100 %

N =    10 %

 t =    33 da

(a) Calculate the value of k

(b) Calculate the half-life

2. Isotope B

Data:

N₀ = 100 %

N =    10 %

 t =    43 da

(a) Calculate the value of k

(b) Calculate the half-life

3. Calculate the difference in half-lives

Difference = 12.9 da - 9.9 da ≈ 3 da

The graphs below show the decay curves for isotopes A and B. The half-lives are approximately 10 da and 13 da, a difference of 3 da.