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### University Physics with Modern Physics

Book edition 14th edition
Author(s) Hugh D. Young, Roger A. Freedman
Pages 1596 pages
ISBN 9780321973610

# In the ${}^{{\mathbf{238}}}{\mathbit{U}}$ decay series shown in Fig. 43.7, some nuclides in the series are found much more abundantly in nature than others, even though every ${}^{{\mathbf{238}}}{\mathbit{U}}$ nucleus goes through every step in the series before finally becoming ${}^{{\mathbf{214}}}{\mathbit{P}}{\mathbit{b}}$. Why don’t the intermediate nuclides all have the same abundance?

The intermediate nuclides all have the same abundance as the time spent in one stage or another is varied enormously.

See the step by step solution

## Step 1: Define the isotopes.

The two or more atoms having the same atomic number and different mass numbers are known as isotopes.

For example: ${}_{8}{}^{16}O$ and ${}_{8}{}^{15}O$

## Step 2: Explain why the intermediate nuclides all have the same abundance?

In a secular equilibrium the activity $A=\lambda N$. As the short half-life $\lambda$ increased the number of nuclei $N$ will decrease.

The time spent in one stage or another is varied enormously.

Hence, the intermediate nuclides all have the same abundance.

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