Chapter 32, Problem 48GP

(a)

To determine

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

Answer to Problem 48GP

The given reaction is possible through the strong interaction.

Explanation of Solution

The given reaction is,

  ${\pi }^{-}+p\to K^{+}+{\sum }^{-}$

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

  ${\pi }^{-}+p\to K^{+}+{\sum }^{-}$

Charge     -1 +1 = +1 -1
Baryon number 0 1 = 0 1
Lepton number 0 0 = 0 0
Strangeness   0 0 = +1 -1

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

Conclusion:

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

(b)

To determine

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

Answer to Problem 48GP

The given reaction is possible through the strong interaction.

Explanation of Solution

The given reaction is,

  ${\pi }^{+}+p\to K^{+}+{\sum }^{+}$

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

  ${\pi }^{+}+p\to K^{+}+{\sum }^{+}$

Charge +1 +1 = +1 +1

Baryon number 0 1 = 0 1

Lepton number 0 0 = 0 0

Strangeness 0 0 = +1 -1

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

Conclusion:

Hence, all conservation law is 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 48GP

The given reaction is possible through the strong interaction.

Explanation of Solution

The given reaction is,

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

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

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

Charge -1 +1 = 0 0 0

Baryon number 0 1 = 1 0 0

Lepton number 0 0 = 0 0 0

Strangeness 0 0 = -1 +1 0

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

Conclusion:

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

(d)

To determine

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

Answer to Problem 48GP

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

Explanation of Solution

The given reaction is,

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

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

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

Charge $+1+1\ne 00$

Charge is not conserved. Therefore, the rection is not possible

Conclusion:

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

(e)

To determine

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

Answer to Problem 48GP

The given reaction is possible through the weak interaction.

Explanation of Solution

The given reaction is,

  ${\pi }^{-}+p\to p+e^{-}+\text{antiparticle}$

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

  ${\pi }^{-}+p\to p+e^{-}+\text{antiparticle}$

Charge -1 +1 = +1 -1 0

Baryon number 0 1 = 1 0 0

Lepton number 0 0 = 0 1 -1

Strangeness 0 0 = 0 0 0

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

Conclusion:

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