Answer:
2.447 × 10⁴ years
Explanation:
Step 1: Given data
- Half-life of the radioactive atom (t1/2): 3,500 years
- Parent-daughter ratio ([A]/[A]₀): 1:127 (1/127)
Step 2: Calculate the rate constant
Radioactive decay follows first-order kinetics. We can calculate the rate constant (k) using the following equation.
k = ln2 / (t1/2) = ln2 / 3,500 y = 1.980 × 10⁻⁴ y⁻¹
Step 3: Calculate the time elapsed (t)
For first-order kinetics, we will use the following expression.
ln ([A]/[A]₀) = -k × t
t = ln ([A]/[A]₀)/ (-k)
t = ln (1/127) / (1.980 × 10⁻⁴ y⁻¹) = 2.447 × 10⁴ y
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