In a sample of pitchblende the ratio of 206 Pb : 238U = 0.2:1 by weight. If the disintegration constant of 238 U is 1.54 ×10^-10 per year and all Pb is supposed to be originated from Uranium, what will be the age of the mineral ?
Answers
Explanation:
Radioisotopes find wide applications in the fields of medicine, agriculture, archeology, engineering, etc.
Age of minerals and rocks
The radioactive properties of uranium-238 (92U238) are used to determine the approximate age of minerals and rocks. Uranium-238 (half-life = 4.5 109 years) disintegrates to stable lead-206 (92Pb206) isotope. The half-life of uranium-238 is longer than that of any other member in the series. Hence, all the uranium-238 disintegrated would have been converted to lead-206.
Assuming that the rock did not contain any lead initially, we can calculate the age of the rock by measuring the ratio of concentrations of 92U238 and 82Pb206. Knowing the ratio of concentrations, , the amount of uranium-238 originally present and the amount of uranium-238 present at the time of analysis can be calculated. From this the age of rock can be calculated by using the equation,
Where,
No is the amount of 92U238 present initially.
N is the amount of 92U238 present after time, t.
l is disintegration constant, which is equal to
This can be better understood with the help of an example.
Example: A sample of pitchblende contains 0.5 g of lead-206 for every gram of uranium-238 present in it. Calculate the age of the pitchblende ore. (half-life of uranium-238 = 4.5 109 years).
