91Ó°ÊÓ

The following interaction is provided

${\mathrm{π}}^{+}+p→p+p+\stackrel{¯}{n}$ ..... (I)

The charge, baryon number and strangeness of ${\mathrm{Ï€}}^{+}$ are as follows

localid="1664343889584" $$\begin{gathered} {\mathbf{Q}}_{{\mathbf{Ï€}}^{\mathbf{+}}}\mathbf{=}\mathbf{+}\mathbf{1} \\ {\mathbf{B}}_{{\mathbf{Ï€}}^{\mathbf{+}}}\mathbf{=}\mathbf{0} \\ {\mathbf{S}}_{{\mathbf{Ï€}}^{\mathbf{+}}}\mathbf{=}\mathbf{0} \end{gathered}$$..... (II)

The charge, baryon number and strangeness of the proton are as follows

localid="1664343883188" $$\begin{gathered} {\mathbf{Q}}_{\mathbf{p}}\mathbf{=}\mathbf{+}\mathbf{1} \\ {\mathbf{B}}_{\mathbf{p}}\mathbf{=}\mathbf{+}\mathbf{1} \\ {\mathbf{S}}_{\mathbf{p}}\mathbf{=}\mathbf{0} \end{gathered}$$ ..... (III)

Let the charge of the antineutron be $Q_{\stackrel{¯}{n}}$. Use charge conservation on the interaction in equation (I) with the values given in equations (II) and (III)

$$\begin{gathered} Q_{{\mathrm{π}}^{+}}+Q_p=Q_p+Q_p+Q_{\stackrel{¯}{n}} \\ +1+1=+1+1+Q_{\stackrel{¯}{n}} \\ {Q}_{\stackrel{¯}{n}}=0 \end{gathered}$$

Thus, the charge is 0.

Let the baryon number of the antineutron be$B_{\stackrel{¯}{n}}$ . Use baryon number conservation on the interaction in equation (I) with the values given in equations (II) and (III)

$$\begin{gathered} B_{{\mathrm{π}}^{+}}+B_p=B_p+B_p+B_{\stackrel{¯}{n}} \\ 0+1=+1+1+B_{\stackrel{¯}{n}} \\ {B}_{\stackrel{¯}{n}}=-1 \end{gathered}$$

Thus, the baryon number is $-1$.

(c)

Let the strangeness of the antineutron be $S_{\stackrel{¯}{n}}$. Use strangeness conservation on the interaction in equation (I) with the values given in equations (II) and (III)

$$\begin{gathered} S_{{\mathrm{π}}^{+}}+S_p=S_p+S_p+S_{\stackrel{¯}{n}} \\ 0+0=0+0+S_{\stackrel{¯}{n}} \\ {S}_{\stackrel{¯}{n}}=0 \end{gathered}$$

Thus, the strangeness is $0$.