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Question

After 3 days a sample of radon-222 has decayed to 58% of its original amount.

1.What is the half-life of radon-222? (Round your answer to two decimal places

2.How long will it take the sample to decay to 30% of its original amount? (Round your answer to two decimal places.)

Answer 1

A = A₀(0.5)^t/h, where A₀ = starting amount, t = time, h = half-life

 

0.58A₀ = A₀(0.5)^3/h                                         divide both sides by A₀

0.58 = (0.5)^3/h                                                take ln of both sides

ln 0.58 = ln (0.5)^3/h                                         law of logarithms

ln 0.58 = (3/h) ln (0.5)                                    calculate ln

-0.544727175 ≈ (3/h) (-0.693147181)           multiply both sides by h

-0.544727175h ≈ (3) (-0.693147181)            simplify right sides

-0.544727175h ≈ -2.07944154                      divide both sides by left coefficient

h ≈ 3.8174

 

The half life is approximately 3.8174 days.

 

Use this value to compute the second problem using the formula at the top.

Answer 2

 

1. 3.82 days

2. 6.63 days