Chapter 20, Problem 35QP

Interpretation Introduction

Interpretation:

The ratio of ${}^{238}\text{U}$

to ${}^{\text{206}}\text{Pb}$ in the given rock sample is to be determined.

Concept introduction:

The amount of a particular radioactive isotope after time t is given as:

$\text{ln}\frac{N_t}{N_o}\text{=}-kt$

Here, $k$

is the rate constant for the radioactive decay, $N_t$ is the amount of it left after time t, and $N_0$ is the initial amount of the sample.

Nearly, all the radioactive decay is of the first order and its rate constant is given as:

$k\text{ = }\frac{0.693}{t_{1/2}}$

Here, $t_{1/2}$

is the half-life of the radioactive substance.