Question

If the half-life of Carbon-14 is 5700 years, how many years would it take a sample to decay from 1 gram to 31.3 mg

Answer 1

Answer:

28500 years

Explanation:

Applying,

A = A'($2^{x/y}$)............... Equation 1

Where A = Original mass of Carbon-14, A' = Final mass of carbon-14 after decaying, x = total time, y = half-life.

From the question,

Given: A = 1 g, A' = 31.3 mg = 0.0313 g, y = 5700 years.

Substitute these values into equation 1

1 = 0.0313($2^{x/5700}$)

$2^{x/5700}$ = 1/0.0313

$2^{x/5700}$  = 31.95

$2^{x/5700}$ ≈ 32

$2^{x/5700}$ ≈ 2⁵

Equating the base and solve for x

x/5700 ≈ 5

x ≈ 5×5700

x ≈ 28500 years