Chapter 32, Problem 49GP

(a)

To determine

To Explain: Whether the given reaction is possible or not.

Answer to Problem 49GP

The given reaction is not possible because charge is not conserved.

Explanation of Solution

The given reaction is,

  ${\pi }^{-}+p\to K^0+p+{\pi }^0$

For the given reaction, the conservation law should be checked, such that

  ${\pi }^{-}+p\to K^0+p+{\pi }^0$

Charge $-1+1\ne 0+10$

Charge is not conserved

Conclusion:

Hence, charge is not conserved by the reaction. So, above reaction is not possible.

(b)

To determine

To Explain: Whether the given reaction is possible or not.

Answer to Problem 49GP

The given reaction is possible through the strong interaction.

Explanation of Solution

The given reaction is,

  $K^{-}+p\to {\Lambda }^0+{\pi }^0$

For the given reaction, the conservation law should be checked, such that

  $K^{-}+p\to {\Lambda }^0+{\pi }^0$

Charge -1 +1 = 0 0

Spin $0+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.0$

Baryon number 0 1 = 1 0

Lepton number 0 0 = 0 0

Strangeness -1 0 = -1 0

Charge is conserved, baryon number and lepton number are also conserved, and strangeness is also conserved.

Conclusion:

Hence, all conservation laws are followed by the reaction. so, above reaction is possible.

(c)

To determine

To Explain: Whether the given reaction is possible or not.

Answer to Problem 49GP

The given reaction is not possible because strangeness is not conserved.

Explanation of Solution

The given reaction is,

  $K^{+}+n\to {\Sigma }^{+}+{\pi }^0+\gamma$

For the given reaction, the conservation law should be checked, such that

  $K^{+}+n\to {\Sigma }^{+}+{\pi }^0+\gamma$

Charge 1 0 = +1 0 0

Spin $0+\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.=-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.01$

Baryon number 0 1 = 1 0 0

Lepton number 0 0 = 0 0 0

Strangeness $10\ne -100$

Charge is conserved, baryon number and lepton number are also conserved, but strangeness is not also conserved.

Conclusion:

Hence, the above reaction is not possible.

(d)

To determine

To Explain: Whether the given reaction is possible or not.

Answer to Problem 49GP

The given reaction is not possible because strangeness is not conserved in the given reaction but it is possible through the weak interaction.

Explanation of Solution

The given reaction is,

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

For the given reaction, the conservation law should be checked, such that

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

Charge 1 = 0 0 0

Spin $0=0+0+0$

Baryon number 0 = 0 0 0

Lepton number 0 = 0 0 0

Strangeness $1\ne 0+0+0$

Strangeness is not conserved.

Conclusion:

Hence, reaction is not allowed but possible through the weak interaction.

(e)

To determine

To Explain: Whether the given reaction is possible or not.

Answer to Problem 49GP

The given reaction is possible through the weak interaction.

Explanation of Solution

The given reaction is,

  ${\pi }^{+}\to e^{+}+v_e$

For the given reaction, the conservation law should be checked, such that

  ${\pi }^{+}\to e^{+}+v_e$

Charge 1 = +1 +0

Spin 0 = +1/2 -1/2

Baryon number 0 = 0 + 0

Lepton number 0 = -1 +1

Strangeness 0 = 0 0

Charge is conserved, baryon number and lepton number are also conserved, and strangeness is also conserved but it is possible through the weak interaction.

Conclusion:

Hence, all conservation law are followed by the reaction. so, above reaction is possible.