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Expert-verified Found in: Page 1302 ### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718 # Figure 42-18 is a plot of mass number A versus charge number Z. The location of a certain nucleus is represented by a dot. Which of the arrows extending from the dot would best represent the transition were the nucleus to undergo (a) a ${\mathbit{\beta }}$ decay and (b) a ${\mathbit{\alpha }}$ decay? 1. The arrows that would represent best for the nucleus that were to undergo $\beta$ decay are d and h.
2. The arrows that would represent best for the nucleus that were to undergo $\alpha$ decay is g.
See the step by step solution

## Step 1: Given data

Figure 42-18 shows the graph of a mass number versus atomic number.

## Step 2: Understanding the concept of decay

There are two decays that the radionuclides mostly undergo. That is an alpha decay and beta decay.

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and also a different nucleus with a mass number that is reduced by four and an atomic number that is reduced by two.

Beta decay is a radioactive decay in which a beta ray is emitted from an atomic nucleus. During beta decay, the proton in the nucleus is transformed into a neutron or vice versa. If a proton is converted to neutron, it is known as beta-plus decay. Similarly, if a neutron is converted to a proton, it is known as beta-minus decay.

## Step 3: a) Calculation of the arrows that represent beta decay

The radioactive decay of a nuclide through beta decay process are of two types. They are beta-minus decay and beta-plus decay.

The beta-minus decay is decay with products as a different nuclide, an electron and an anti-neutrino. That can be given as: ${}_{z}^{A}M\to {}_{z+1}^{A}N+{e}^{-}+\overline{v}$

In the graph, the arrow may undergo beta-minus decay as their atomic number is increasing without any change to the mass number.

The beta-plus decay is decay with products as a different nuclide, a positron and a neutrino. That can be given as: ${}_{z}^{A}M\to {}_{z-1}^{A}N+{e}^{-}+\overline{v}$

In the graph, the arrow may undergo beta-minus decay as their atomic number is increasing without any change to the mass number.

Hence, the arrows that represent beta decay are d and h.

## Step 4: b) Calculation of the arrows that represent alpha decay

An alpha decay of a ${}_{z}^{A}\mathrm{M}$ nuclide can be given as:

${}_{z}^{A}M\to {}_{z+1}^{A-4}N+{}_{2}^{4}He\left(\alpha -particle\right)$

Here, the nuclides undergo a decrease in both the mass and atomic number simultaneously.

Hence, the arrow that best represent the alpha decay is g. ### Want to see more solutions like these? 