Answered

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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

Sagot :

asuwafohjames

Answer:

28500 years

Explanation:

Applying,

A = A'([tex]2^{x/y}[/tex])............... 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([tex]2^{x/5700}[/tex])

[tex]2^{x/5700}[/tex] = 1/0.0313

[tex]2^{x/5700}[/tex]  = 31.95

[tex]2^{x/5700}[/tex] ≈ 32

[tex]2^{x/5700}[/tex] ≈ 2⁵

Equating the base and solve for x

x/5700 ≈ 5

x ≈ 5×5700

x ≈ 28500 years

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