Suppose a sample of a certain substance decayed to 77.6% of its original amount after 300 days.

Question

(Round your answers to two decimal places.) (a) What is the half-life (in days) of this substance?

b. How long would it take the sample to decay to one-third of its original amount?

Answer 1

N = N₀b^t; 0.776N₀ = N₀b³⁰⁰; b³⁰⁰ = 0.776; b= (0.776)^1/300.

(a) 0.5N₀ = N₀(0.776)^t/300; t/300 = ln0.5/ln0.776; t = 300ln0.5/ln0.776 = 820 days(half-life time)

(b) 1/3N₀ = N₀(0.776)^t/300; t = 300ln(1/3)/ln0.776 = 1300 days