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Chapter 16: Problem 13

Positron emission moves us one step to the left in the periodic table, and alpha emission moves us two steps to the left. Does this mean that, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is the same as the daughter isotope resulting from one alpha emission?

Short Answer

Expert verified
No, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is not the same as the daughter isotope resulting from one alpha emission. After two positron emissions, the isotope becomes (Z-2, A), while after one alpha emission, the isotope becomes (Z-2, A-4). The atomic numbers are the same, but the mass numbers are different.

Step by step solution

01

Decay Definitions

Before proceeding, let's define the decay processes. - Positron emission: A positron is emitted when a proton in the nucleus transforms into a neutron. This results in a decrease in the atomic number (Z) by 1, leaving the mass number (A) unchanged. - Alpha emission: An alpha particle consists of 2 protons and 2 neutrons. During alpha emission, the nucleus loses an alpha particle, decreasing both the atomic number (Z) and the mass number (A) by 2 and 4, respectively.
02

Two Positron Emissions

Suppose the parent isotope has atomic number Z and mass number A. After the first positron emission, the atomic number (Z) decreases by 1, but the mass number (A) remains the same. So, the isotope becomes (Z-1, A). After the second positron emission, the atomic number (Z) decreases by 1 once more. Therefore, the resulting isotope after two successive positron emissions becomes (Z-2, A).
03

One Alpha Emission

For the same parent isotope with atomic number Z and mass number A, we will now consider the alpha emission case. During alpha emission, the atomic number (Z) decreases by 2, and the mass number (A) decreases by 4. So, the resulting isotope is (Z-2, A-4).
04

Comparison

Now, we will compare the daughter isotopes from both cases to determine if they are the same or not. - Two successive positron emissions: (Z-2, A) - One alpha emission: (Z-2, A-4) The atomic numbers for both daughter isotopes are the same (Z-2) but the mass numbers are different (A and A-4). So, the daughter isotopes are not the same. Thus, for a given parent isotope, the daughter isotope resulting from two successive positron emissions is not the same as the daughter isotope resulting from one alpha emission.

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Complete this nuclear reaction, and name the decay process: \({ }_{4}^{8} \mathrm{Be}+? \rightarrow{ }_{3}^{8} \mathrm{Li}\)

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