Chapter 30, Problem 31P

(a)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is not conserved.

Explanation of Solution

The reaction is,

${\Lambda }^0\to p+{\pi }^{+}$

A strangeness of ${\Lambda }^0$ is -1, the strangeness of $p$ is 0 and the strangeness of ${\pi }^{+}$ is 0.

Therefore,

$\begin{array}{c}-1\to 0+0\\ -1\to 0\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=-1-0\\ =-1\\ \ne 0\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is not conserved.

Conclusion:

The strangeness is not conserved.

(b)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is conserved.

Explanation of Solution

The reaction is,

${\pi }^{+}+p\to {\Lambda }^0+K^{+}$

A strangeness of ${\Lambda }^0$ is -1, the strangeness of $p$ is 0 , the strangeness of $K^0$ is +1 and the strangeness of ${\pi }^{+}$ is 0.

Therefore,

$\begin{array}{c}0+0\to -1+1\\ 0\to 0\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=0-0\\ =0\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is conserved.

Conclusion:

The strangeness is conserved.

(c)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is conserved.

Explanation of Solution

The reaction is,

$\overline{p}+p\to \overline{{\Lambda }^0}+{\Lambda }^0$

A strangeness of ${\Lambda }^0$ is -1, the strangeness of $p$ is 0 , the strangeness of $\overline{{\Lambda }^0}$ is +1 and the strangeness of $\overline{p}$ is 0.

Therefore,

$\begin{array}{c}0+0\to -1+1\\ 0\to 0\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=0-0\\ =0\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is conserved.

Conclusion:

The strangeness is conserved.

(d)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is not conserved.

Explanation of Solution

The reaction is,

${\pi }^{-}+p\to {\pi }^{-}+{\Sigma }^{+}$

A strangeness of ${\pi }^{-}$ is 0, the strangeness of $p$ is 0 , the strangeness of ${\pi }^{-}$ is 0 and the strangeness of ${\Sigma }^{+}$ is -1.

Therefore,

$\begin{array}{c}0+0\to 0-1\\ 0\to -1\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=-1-0\\ =-1\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is not conserved.

Conclusion:

The strangeness is not conserved.

(e)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is not conserved.

Explanation of Solution

The reaction is,

${\Xi }^{-}\to {\Lambda }^0+{\pi }^{-}$

A strangeness of ${\Lambda }^0$ is -1, the strangeness of ${\Xi }^{-}$ is -2 and the strangeness of ${\pi }^{-}$ is 0.

Therefore,

$\begin{array}{c}-2\to -1+0\\ -2\to -1\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=-2--1\\ =-1\\ \ne 0\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is not conserved.

Conclusion:

The strangeness is not conserved.

(f)

To determine

The conservation of strangeness in the reaction.

Answer to Problem 31P

The strangeness is not conserved.

Explanation of Solution

The reaction is,

${\Xi }^{-}\to p+{\pi }^{-}$

A strangeness of $p$ is 0, the strangeness of ${\Xi }^{-}$ is -2 and the strangeness of ${\pi }^{-}$ is 0.

Therefore,

$\begin{array}{c}-2\to 0+0\\ -2\to 0\end{array}$

The difference in strangeness in the reaction is,

$\begin{array}{c}\Delta s=-2-0\\ =-2\\ \ne 0\end{array}$

• $\Delta s$ is the variation in strangeness in each side of the reaction

Thus, the strangeness is not conserved.

Conclusion:

The strangeness is not conserved.