Answer:
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.
Step-by-step 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