Which represents the balanced nuclear equation for the beta plus decay of C-11?
${ }_6^{11} C \longrightarrow{ }_5^{11} B+{ }_{+1}^0 e$
${ }_6^{11} C \longrightarrow{ }_7^{11} N+{ }_{+1}^0 e$
${ }_6^{11} C \longrightarrow{ }_7^{11} N+{ }_{-1}^0 e$
${ }_6^{11} C \longrightarrow{ }_5^{11} B+{ }_{-1}^0 e
Answer (2)
Beta plus decay involves the emission of a positron, changing a proton into a neutron.
Conserve mass number: 11 = A + 0 , so A = 11 .
Conserve atomic number: 6 = Z + 1 , so Z = 5 , which corresponds to Boron (B).
The balanced nuclear equation is: 6 11 C ⟶ 5 11 B + + 1 0 e .
Explanation
Understanding Beta Plus Decay We are given four options for the beta plus decay of Carbon-11 (C-11) and need to identify the correct balanced nuclear equation. In beta plus decay, a proton in the nucleus is converted into a neutron, and a positron ( + 1 0 e ) is emitted. The general form of a beta plus decay equation is Z A X ⟶ Z − 1 A Y + + 1 0 e , where X is the parent nucleus, Y is the daughter nucleus, A is the mass number, and Z is the atomic number.
Setting up the Equation For the beta plus decay of C-11, the parent nucleus is 6 11 C . Thus, the equation will be of the form 6 11 C ⟶ Z A Y + + 1 0 e . We need to find the values of A and Z for the daughter nucleus Y.
Conserving Mass and Atomic Numbers The mass number (A) must be conserved. Therefore, 11 = A + 0 , which means A = 11 . The atomic number (Z) must also be conserved. Therefore, 6 = Z + 1 , which means Z = 5 .
Identifying the Daughter Nucleus The element with atomic number 5 is Boron (B). So, the daughter nucleus is 5 11 B . Therefore, the balanced nuclear equation for the beta plus decay of C-11 is 6 11 C ⟶ 5 11 B + + 1 0 e .
Final Answer Comparing the derived equation with the given options, we find that the first option matches our result: 6 11 C ⟶ 5 11 B + + 1 0 e .
Examples
Beta decay is a crucial concept in nuclear medicine, particularly in Positron Emission Tomography (PET) scans. In PET scans, radioactive isotopes that undergo beta plus decay are used as tracers. These isotopes emit positrons, which then annihilate with electrons in the body, producing gamma rays that are detected by the scanner. By analyzing the distribution of these gamma rays, doctors can create detailed images of organs and tissues, helping to diagnose diseases like cancer, heart disease, and neurological disorders. The balanced nuclear equation helps in understanding the transformation of the radioactive isotope during the decay process.
The balanced nuclear equation for the beta plus decay of Carbon-11 (C-11) is 6 11 C ⟶ 5 11 B + + 1 0 e . This reflects the transformation of a proton into a neutron, emitting a positron. Therefore, the correct choice is the first option.
;
