Chapter U1, Problem 13STP

Interpretation Introduction

Interpretation:

The amount of original sample of carbon-14 remains after two half-lives needs to be determined, if 10.0 g of sample is taken.

Concept introduction:

Nuclear reactions are a type of chemical processes which lead to the formation of some new nuclei with the emission of certain particles. Alpha rays, beta rays and gamma rays are emitted with some new daughter nuclei during these reactions.

The nuclei which show spontaneous decay with time are called as radioactive nuclei. The radioactive decay follows the first order kinetic and the half-life is inversely proportional to the decay constant of the radioactive decay.

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{ = }\frac{\text{0}\text{.693}}{\text{λ}}\\ \text{here:}\\ {\text{t}}_{\text{1/2}}\text{ = half-life}\\ \text{λ = decay constant}\end{array}$

Answer to Problem 13STP

Option (D) is correct.

Explanation of Solution

Reason for correct option:

Initial amount of sample = 10.0 g

Half-life indicates the time in which the sample decays half of its original amount. Hence after two half-lives,

Conclusion

Reasons for incorrect options:

Two half-lives will decay ¼ of the original sample, thus option (A), (B) and (C) are incorrect.