Chapter 18, Problem 29E

Interpretation Introduction

Interpretation: Mass of ${}^{\text{47}}{\text{CaCO}}_{\text{3}}$ required for $\text{5μg}$ of the ${}^{\text{47}}{\text{Ca}}^{\text{2+}}$ nuclide in the given experiment is to be stated.

Concept introduction: A process through which a unstable nuclide looses its energy due to excess of protons or neutrons is known as radioactive decay. The cause of instability of a nuclide is its inefficiency in holding the nucleus together.

Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second. Half life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

The decay constant can be calculated by the formula given below.

$\lambda =\frac{0.693}{{\text{t}}_{1/2}}$

The time of decay can be calculated by the formula given below

$t=\frac{2.303}{\lambda }\log \frac{n_0}{n}$

To determine: Mass of ${}^{\text{47}}{\text{CaCO}}_{\text{3}}$ required for $\text{5μg}$ of the ${}^{\text{47}}{\text{Ca}}^{\text{2+}}$ nuclide in the given experiment.