Question

The half-life of Carbon- $ 14 $ is $ 5715yr $ . What is its decay constant?

Answer 1

Hint :Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.

Complete Step By Step Answer:
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
Half-life of carbon- $ 14 $ = $ 5715yr $
We have to find the decay constant
We have the equation for half-life,
 $ {t_{1/2}} = 0.693/\lambda $
Where, $ {t_{1/2}} $ is the half-life and $ \lambda $ is the decay constant.
So, $ \lambda = 0.693/5715 = 0.0001212598 $

Note :
Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles or photons. The weak force is the mechanism that is responsible for beta decay, while the other two are governed by the usual electromagnetic and strong forces.