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Chapter 16: Problem 11

The magnesium isotope \({ }_{12}^{25} \mathrm{Mg}\) is the daughter isotope created when a radioactive parent isotope undergoes positron emission. What is the full symbol for the parent isotope?

Short Answer

Expert verified
The full symbol for the parent isotope is \(_{12}^{25} \mathrm{Mg}\).

Step by step solution

01

Understanding positron emission

Positron emission occurs when a proton in a nucleus is converted into a neutron, resulting in the emission of a positron. As a result, the atomic number decreases by 1 while the mass number (the total number of protons and neutrons) remains the same.
02

Writing the nuclear equation for positron emission

In a positron emission, the nucleus X gives rise to a daughter nucleus Y and a positron. We can write the nuclear equation as: \[_{Z}^A \text{X} \rightarrow_{Z-1}^A \text{Y} + _{1}^{0} e\] In this case, the daughter nucleus is \({}_{12}^{25} \mathrm{Mg}\). Plugging this into the equation, we get: \[_{Z}^A \text{X} \rightarrow_{11}^{25} \mathrm{Y} + _{1}^{0} e\]
03

Determine the parent isotope

Based on the nuclear equation, we can determine the parent isotope X by knowing the atomic number (Z) and mass number (A) of the daughter isotope. The mass number A remains the same after positron emission, so \(A=25\). The atomic number decreases by 1 during positron emission, so the parent isotope's atomic number \(Z=11+1 = 12\). Now, we can write the full symbol for the parent isotope: \[_{12}^{25} \text{X}\] The element with atomic number 12 is magnesium (Mg). The full symbol for the parent isotope is: \[_{12}^{25} \mathrm{Mg}\]

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