Chapter 29, Problem 6RQ

What are the half-lives of uranium-238, potassium-40 and carbon-14?

To determine

The half-lives of uranium-238, potassium-40 and Carbon-14.

Answer to Problem 6RQ

The half-life of uranium-238 is $4.5$ billion years, potassium-40 is $1.3$ billion years and carbon-14 is $5760$ years.

Explanation of Solution

The nucleus of the radioactive elements is not stable. They have the tendency to release alfa and beta particles and try to come in a stable position. During decay, radioactive elements release a huge amount of energy, which can also be used for power generation.

Old rocks can contain some of the radioactive elements like uranium-238, potassium-40, and Carbon-14. Out of these, Carbon-14 has the least value of half-life.

The half-life of uranium-238 is $4.5$ billion years, and its stable daughter product is Lead-206. The half-life of potassium-40 is $1.3$ billion years, and its stable daughter product is Argon-40. The half-life of carbon-14 is $5760$ years, and its stable daughter product is nitrogen-14.

Conclusion:

Therefore, the half-life of uranium-238 is $4.5$ billion years, potassium-40 is $1.3$ billion years and Carbon-14 is $5760$ years.