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Natasha_Volkova [10]
3 years ago
12

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

Chemistry
1 answer:
andrew-mc [135]3 years ago
3 0

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

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