Question

1. Applications of radioactive decay extend beyond potential terrorism. There are a number of regularly used practical applications. One such application is to use radioactive decay as a mechanism for determining the age of a sample of bones, rocks, meteorites, etc. Say you area scientist tasked with analyzing samples of moon rocks. Your moon rock contains small amounts of Uranium-238. U-238 decays into lead-206 with a half-life of 4.5 billion years. How old is your rock if 55.0% of the original U-238 remains at the time you tested the rock. (Hint: this can be done using equations discussed in chapter 12).

Answer 1

Half-life Uranium 238 is 4.5 billion years i.e., say 100 g of U-238 decays to 50g in 4.5 billion years.

Amount of original U-238 remaining in the sample at the time of testing is 55%.

Time elapsed can be calculated using the following expression:

t = ln (Nt/No) / -$\lambda$

Where t is time elapsed

Nt = % of U-238 at time t i.e., 55

No = % of U-238 at time 0 i.e., 100

$\lambda$ = No. of disintegrations = ln(2) / half-life = 0.69315 / 4.5 x 109 years = 0.15403 x 10-9 years-1

Time elapsed = ln (55/100) / (-0.15403 x 10-9 years-1)

= ln (0.55) / (-0.15403 x 10-9 years-1)

= ln (0.55) / (-0.15403 x 10-9 years-1)

= -0.59783 / (-0.15403 x 10-9 years-1)

= (0.59783 / 0.15403) x 109 years

Time elapsed = 3.8812 x 109 years i.e., 3.8812 billion years

Answer: The moon rock is 3.8812 biillion years old based on the data provided. (U-238 half-life is 4.5 billion years and amount U-238 remaining in the moon rock is 55%)