Question

Question: Write the balanced equations for the decays of ${}^{\mathbf{11}}\mathbf{C}$and ${}^{\mathbf{15}}\mathbf{O}$, both of which are used in positron emission tomography to scan the uptake of glucose in the body.

Short answer

The balanced equations for the decays of ${}^{11}\mathrm{C}$and data-custom-editor="chemistry" ${}^{15}\mathrm{O}$are given below.

• ${}_6{}^{11}\mathrm{C}\to {}_5{}^{11}\mathrm{B}+{{}_1{}^{0}e}^{+}+V$
  
• localid="1660974050534" ${}_8{}^{15}\mathrm{O}\to {}_7{}^{15}\mathrm{B}+{{}_1{}^0\mathrm{e}}^{+}+\mathrm{V}$
  

Step-by-step solution

Brief introduction to PET

PET is an abbreviation for positron emission tomography. The radioisotopes used in PET scan are ${}^{11}\mathrm{C},{}^{13}\mathrm{N},{}^{15}\mathrm{O}$and ${}^{18}\mathrm{F}$. When positrons and electrons collide , they annihilate each other and the resultant radiations emitted are known as annihilation radiations. From the emitted photons, the positron emission tomography traces back the location of the radioisotopes to detect the position of the tumor or any other abnormality.

Positron emission byC11

When a positron emission takes place, a proton is transformed into a neutron. A neutrino is also emitted along with a positron. The mass number of the daughter nuclei remains the same as that of the parent nucleus, but the atomic number of the daughter nuclei is one less than that of the parent nuclei. The balanced nuclear equation representing positron emission by ${}^{11}\mathrm{C}$is:

${}_6{}^{11}\mathrm{C}\to {}_5{}^{11}\mathrm{B}+{{}_1{}^{0}e}^{+}+V$

Positron emission by O15

When positron emission takes place ${}^{15}\mathrm{O}$decays into ${}^{15}\mathrm{N}$. A neutrino is also emitted along with a positron. The balanced equation representing the nuclear reaction is:

${}_8{}^{15}\mathrm{O}\to {}_7{}^{15}\mathrm{B}+{{}_1{}^0\mathrm{e}}^{+}+\mathrm{V}$