Question 10.3: Write a balanced nuclear equation for the positron emission ...
Write a balanced nuclear equation for the positron emission of fluorine-18, a radioisotope used for imaging in PET scans.
Analysis
Balance the atomic numbers and mass numbers on both sides of a nuclear equation. With \beta^{+} emission, treat the positron as a particle with zero mass when balancing mass numbers and a + 1 charge when balancing the atomic numbers.
[1] Write an incomplete equation with the original nucleus on the left and the particle emitted on the right.
• Use the identity of the element to determine the atomic number; fluorine has an atomic number of 9.
{ }_9^{18} \mathrm{~F} \longrightarrow{ }_{+1}^0 e+\text { ? }[2] Calculate the mass number and the atomic number of the newly formed nucleus on the right.
• Mass number: Since a \beta^{+} particle has no mass, the masses of the new particle and the original particle are the same, 18.
• Atomic number: Since \beta^{+} emission converts a proton into a neutron, the new nucleus has one fewer proton than the original nucleus; 9 − 1 = 8. Thus, the new nucleus has an atomic number of 8.
[3] Use the atomic number to identify the new nucleus and complete the equation.
• From the periodic table, the element with an atomic number of 8 is oxygen, O.
• Write the mass number and the atomic number with the element symbol to complete the equation.