To determine the balanced equation for the beta minus (β⁻) emission of phosphorus-32, we need to understand what happens during a beta minus decay. In beta minus decay, a neutron in the nucleus of an atom is converted to a proton, releasing an electron (β⁻ particle) and an antineutrino.
The atomic number of the element increases by 1 (as a neutron turns into a proton), but the mass number remains unchanged (since the neutron is replaced by a proton).
Phosphorus-32 [tex]\(_{15}^{32}P\)[/tex] has an atomic number of 15 and a mass number of 32.
In beta minus decay, phosphorus-32 will transform into an element with an atomic number of 16 (one more than 15) but with the same mass number of 32.
Thus, the element formed will be sulfur-32 [tex]\(_{16}^{32}S\)[/tex], and a beta particle [tex]\(_{-1}^0e\)[/tex] (an electron) will be emitted.
So, the balanced equation for the beta minus emission of phosphorus-32 is:
[tex]\[
_{15}^{32}P \longrightarrow \ _{16}^{32}S + \ _{-1}^0e
\][/tex]
This corresponds to the equation:
[tex]\[
_{15}^{32}P \longrightarrow \ _{16}^{32}S+ \ _{-1}^0 e
\][/tex]
