Chapter 31, Problem 26P

(a)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are baryon number, charge, electron lepton number and tau lepton number.

Explanation of Solution

Write the reaction.

    ${\Xi }^{-}\to {\Lambda }^0+{\mu }^{-}+{\nu }_{\mu }$

Check the conservation of baryon number for the reaction on both sides.

    $1\to 1+0+0$

Check the conservation of charge for the reaction on both sides.

    $-1\to 0-1+0$

Check the conservation of electron lepton number for the reaction on both sides.

    $0\to 0+0+0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0\to 0+1+1$

Check the conservation of tau lepton number for the reaction on both sides.

    $0\to 0+0+0$

Check the conservation of strangeness for the reaction on both sides.

    $-2\to -1+0+0$

Conclusion:

Thus, the conserved quantities in the reaction are baryon number, charge, electron lepton number and tau lepton number.

(b)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number and tau lepton number.

Explanation of Solution

Write the reaction.

    ${\text{K}}_{\text{S}}^0\to 2{\pi }^0$

Check the conservation of baryon number for the reaction on both sides.

    $0\to 0$

Check the conservation of charge for the reaction on both sides.

    $0\to 0$

Check the conservation of electron lepton number for the reaction on both sides.

    $0\to 0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0\to 0$

Check the conservation of tau lepton number for the reaction on both sides.

    $0\to 0$

Check the conservation of strangeness for the reaction on both sides.

    $+1\to 0$

Conclusion:

Thus, the conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number and tau lepton number.

(c)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

Explanation of Solution

Write the reaction.

    ${\text{K}}^{-}+p\to {\Sigma }^0+n$

Check the conservation of baryon number for the reaction on both sides.

    $0+1\to 1+1$

Check the conservation of charge for the reaction on both sides.

    $-1+1\to 0+0$

Check the conservation of electron lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of tau lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of strangeness for the reaction on both sides.

    $-1+0\to -1+0$

Conclusion:

Thus, the conserved quantities in the reaction are charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

(d)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

Explanation of Solution

Write the reaction.

    ${\Sigma }^0\to {\Lambda }_0+\gamma$

Check the conservation of baryon number for the reaction on both sides.

    $1\to 1+0$

Check the conservation of charge for the reaction on both sides.

    $0\to 0+0$

Check the conservation of electron lepton number for the reaction on both sides.

    $0\to 0+0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0\to 0+0$

Check the conservation of tau lepton number for the reaction on both sides.

    $0\to 0+0$

Check the conservation of strangeness for the reaction on both sides.

    $-1\to -1+0$

Conclusion:

Thus, the conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

(e)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

Explanation of Solution

Write the reaction.

    $e^{+}+e^{-}\to {\mu }^{+}+{\mu }^{-}$

Check the conservation of baryon number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of charge for the reaction on both sides.

    $1-1\to 1-1$

Check the conservation of electron lepton number for the reaction on both sides.

    $-1+1\to 0+0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0+0\to 1-1$

Check the conservation of tau lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of strangeness for the reaction on both sides.

    $0+0\to 0+0$

Conclusion:

Thus, the conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

(f)

To determine

The conserved quantities in the reaction.

Answer to Problem 26P

The conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

Explanation of Solution

Write the reaction.

    $\overline{p}+n\to {\overline{\Lambda }}^0+{\Sigma }^{-}$

Check the conservation of baryon number for the reaction on both sides.

    $-1+1\to -1+1$

Check the conservation of charge for the reaction on both sides.

    $-1+0\to 0-1$

Check the conservation of electron lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of muon lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of tau lepton number for the reaction on both sides.

    $0+0\to 0+0$

Check the conservation of strangeness for the reaction on both sides.

    $0+0\to 1-1$

Conclusion:

Thus, the conserved quantities in the reaction are baryon number, charge, electron lepton number, muon lepton number, tau lepton number and strangeness.

(g)

To determine

The reactions that cannot occur.

Answer to Problem 26P

The reactions that cannot occur are (a), (b) and (c).

Explanation of Solution

Write the reaction (a).

    ${\Xi }^{-}\to {\Lambda }^0+{\mu }^{-}+{\nu }_{\mu }$

Reaction (a) cannot occur because muon lepton number and strangeness are not conserved.

Write the reaction (b).

    ${\text{K}}_{\text{S}}^0\to 2{\pi }^0$

Reaction (b) cannot occur because strangeness is not conserved.

Write the reaction (c).

    ${\text{K}}^{-}+p\to {\Sigma }^0+n$

Reaction (c) cannot occur because baryon number is not conserved.

Conclusion:

Thus, the reactions that cannot occur are (a), (b) and (c).