The half life for the radioactive decay of carbon- to nitrogen- is years. Suppose nuclear chemical analysis shows that there is of nitrogen- for every of carbon- in a certain sample of rock. Calculate the age of the rock. Round your answer to significant digits. g

Age of rock = 6.12 × 10³ years

Note: The question is incomplete.A similar but complete question is given below.

The half-life for the radioactive decay of carbon-14 to nitrogen-14 is 5.73 x 10^3 years. Suppose nuclear chemical analysis shows that there is 0.523mmol of nitrogen-14 for every 1.000 mmol of carbon-14 in a certain sample of rock.

Calculate the age of the rock. Round your answer to 2 significant digits.

Explanation:

The half-life of a radioactive material is the time taken for half the atoms in the atomic nucleus of a material to disintegrate.

The half-life for the radioactive decay of carbon-14 to nitrogen-14 is given as 5.73 x 10³ years. This means that given 1 mole of carbon-14 is present initially, after one half-life, 0.5 moles of carbon-14 would remain.

Number of millimoles of carbon-14 remaining = 1 - 0.523 = 0.477 mmol

Number of half-lives that the carbon-14 has undergone is determined as follows:

Amount remaining = (1/2)ⁿ

where nnis number of half-lives

0.5 mmol = one half-life

0.5 = (1/2)¹

O.477 = (1/2)ⁿ = (0.5)ⁿ

㏒₀.₅(0.477) = n

n = ㏒(0.477)/㏒(0.5)

n = 1.067938829

Age of the rock = number of half-lives × half-life

Age of rock = 1.067938829 × 5.73 × 10³ years

Age of rock = 6.12 × 10³ years

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