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fiasKO [112]
3 years ago
10

If the half-life of a radioactive atom is 3,500 years. How old is the substance if the parent-daughter ratio is 1:127?

Biology
1 answer:
balu736 [363]3 years ago
3 0

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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