Question

The isotope Beryllium-10 decays to Boron-10 over a half-life of 1.5 million years. These isotopes would have experienced four half lives in igneous rocks that were 6 million years old. Select one: True False

Answer 1

Answer:

Number of half lives experienced by an isotope was 4,so the given statement is true.

Explanation:

The initial amount of isotope Beryllium-10  = [A_o][/tex]

Final amount of isotope Beryllium-10 after time t = [A]

t = 6 million years

Half life of the sample = $t_{1/2}$ = 1.5 million years

Decay constant of the process = $\lambda = \frac{0.693}{t_{1/2}}$

Integrated law of first order reaction:

$[A]=[A_o]\times e^{-\lambda t}$

$[A]=[A_o]\times ^{-\frac{0.693}{1.5 \text{million years}}\times 6.0\text{million years}}$

$[A]=0.06254 [A_o]$

Number of half lives elapsed be n:

$[A]=\frac{[A_o]}{2^n}$        ............(1)

$0.06254 [A_o]=\frac{[A_o]}{2^n}$

Solving fro n:

n = 3.999 ≈ 4

Number of half lives experienced by an isotope was 4,so the given statement is true.