Assuming that 89% of the disintegrations of 40 K result in ẞ- emission, and that the 19 normal abundance of 40 K in a sample of pure potassium is 0.012%, calculate the number of beta particles emitted per second by a crystal of potassium chloride (KCI) whose mass is 5.0 g. The atomic masses of potassium and chlorine may be taken as 39.1 and 35.5, respectively, and the half-life of 40 K is 1.28 × 10º years. In the mixture of isotopes normally found on the earth at the present time, 238U has an abundance of 99.3% and 235U has an abundance of 0.7%. The measured lifetimes of these radioactive isotopes are 6.52 × 10⁹ y and 1.02 × 10⁹ y, respectively. By assuming that they were equally abundant when the uranium in the earth was originally formed, estimate how much time has elapsed since the time of formation. How does the estimated age of the earth obtained from this simple argument compare with that obtained from more sophisticated geological and cosmological arguments?

Assuming that 89% of the disintegrations of 40 K result in ẞ- emission, and that the 19 normal abundance of 40 K in a sample of pure potassium is 0.012%, calculate the number of beta particles emitted per second by a crystal of potassium chloride (KCI) whose mass is 5.0 g. The atomic masses of potassium and chlorine may be taken as 39.1 and 35.5, respectively, and the half-life of 40 K is 1.28 × 10º years. In the mixture of isotopes normally found on the earth at the present time, 238U has an abundance of 99.3% and 235U has an abundance of 0.7%. The measured lifetimes of these radioactive isotopes are 6.52 × 10⁹ y and 1.02 × 10⁹ y, respectively. By assuming that they were equally abundant when the uranium in the earth was originally formed, estimate how much time has elapsed since the time of formation. How does the estimated age of the earth obtained from this simple argument compare with that obtained from more sophisticated geological and cosmological arguments?