Chapter 31, Problem 15P

(a)

To determine

Identify the conservation which is violated for the reaction $\text{p}+\overline{\text{p}}\to {\mu }^{+}+{\text{e}}^{-}$.

Answer to Problem 15P

Muon lepton number and electron lepton number are not conserved for $\text{p}+\overline{\text{p}}\to {\mu }^{+}+{\text{e}}^{-}$.

Explanation of Solution

Check for the charge conservation.

    $C:0+0\to 1+-1$

Thus, charge is conserved.

Check for Baryon number conservation.

    $B:\left(+1\right)+\left(-1\right)\to 0+0$

Thus, baryon number is conserved.

Check for electron lepton number conservation.

    $L_e\text{:}0+0\to 0+1$

Thus, electron lepton number is not conserved.

Check for muon lepton number conservation.

    $L_{\mu }\text{:}0+0\to -1+0$

Thus, muon lepton number is not conserved.

Check for tau lepton number conservation.

    $L_{\tau }\text{:}0+0\to 0+0$

Thus, tau lepton number is conserved.

Check for strangeness number conservation.

    $S:0+0\to 0+0$

Conclusion:

Therefore, the muon lepton number and electron lepton number are not conserved $\text{p}+\overline{\text{p}}\to {\mu }^{+}+{\text{e}}^{-}$.

(b)

To determine

Identify the conservation which is violated for the reaction $\text{p}+\overline{\text{p}}\to {\mu }^{+}+{\text{e}}^{-}$.

Answer to Problem 15P

Charge is not conserved for ${\pi }^{-}+\text{p}\to \text{p}+{\pi }^{+}$.

Explanation of Solution

Check for the charge conservation.

    $C:-1+0\to 1+\left(+1\right)$

Thus, charge is not conserved.

Check for Baryon number conservation.

    $B:0+0\to 0+0$

Thus, baryon number is conserved.

Check for electron lepton number conservation.

    $L_e\text{:}0+0\to 0+0$

Thus, electron lepton number is conserved.

Check for muon lepton number conservation.

    $L_{\mu }\text{:}0+0\to 0+0$

Thus, muon lepton number is conserved.

Check for tau lepton number conservation.

    $L_{\tau }\text{:}0+0\to 0+0$

Thus, tau lepton number is conserved.

Check for strangeness number conservation.

    $S:0+0\to 0+0$

Thus, strangeness is conserved.

Conclusion:

Therefore, Charge is not conserved for ${\pi }^{-}+\text{p}\to \text{p}+{\pi }^{+}$.

(c)

To determine

Identify the conservation which is violated for the reaction $\text{p}+\text{p}\to \text{p}+\text{p}+\text{n}$.

Answer to Problem 15P

Baryon number is not conserved for $\text{p}+\text{p}\to \text{p}+\text{p}+\text{n}$.

Explanation of Solution

Check for the charge conservation.

    $C:\left(+1\right)+\left(+1\right)\to \left(+1\right)+\left(+1\right)+0$

Thus, charge is conserved.

Check for Baryon number conservation.

    $B:1+1\to 1+1+1$

Thus, baryon number is not conserved.

Check for electron lepton number conservation.

    $L_e\text{:}0+0\to 0+0+0$

Thus, electron lepton number is conserved.

Check for muon lepton number conservation.

    $L_{\mu }\text{:}0+0\to 0+0+0$

Thus, muon lepton number is conserved.

Check for tau lepton number conservation.

    $L_{\tau }\text{:}0+0\to 0+0+0$

Thus, tau lepton number is conserved.

Check for strangeness number conservation.

    $S:0+0\to 0+0+0$

Thus, strangeness is conserved.

Conclusion:

Therefore, baryon number is not conserved for $\text{p}+\text{p}\to \text{p}+\text{p}+\text{n}$.

(d)

To determine

Identify the conservation which is violated for the reaction $\gamma +\text{p}\to \text{n}+{\pi }^0$.

Answer to Problem 15P

Charge is not conserved for $\gamma +\text{p}\to \text{n}+{\pi }^0$.

Explanation of Solution

Check for the charge conservation.

    $C:0+1\to 0+0$

Thus, charge is not conserved.

Check for Baryon number conservation.

    $B:0+1\to 1+0$

Thus, baryon number is conserved.

Check for electron lepton number conservation.

    $L_e\text{:}0+0\to 0+0$

Thus, electron lepton number is conserved.

Check for muon lepton number conservation.

    $L_{\mu }\text{:}0+0\to 0+0$

Thus, muon lepton number is conserved.

Check for tau lepton number conservation.

    $L_{\tau }\text{:}0+0\to 0+0$

Thus, tau lepton number is conserved.

Check for strangeness number conservation.

    $S:0+0\to 0+0$

Thus, strangeness is conserved.

Conclusion:

Therefore, charge is not conserved for $\gamma +\text{p}\to \text{n}+{\pi }^0$.

(e)

To determine

Identify the conservation which is violated for the reaction ${\nu }_e+\text{p}\to \text{n}+{\text{e}}^{+}$.

Answer to Problem 15P

Electron lepton number is not conserved for ${\nu }_e+\text{p}\to \text{n}+{\text{e}}^{+}$.

Explanation of Solution

Check for the charge conservation.

    $C:0+1\to 0+1$

Thus, charge is conserved.

Check for Baryon number conservation.

    $B:0+1\to 1+0$

Thus, baryon number is conserved.

Check for electron lepton number conservation.

    $L_e\text{:}1+0\to 0-1$

Thus, electron lepton number is not conserved.

Check for muon lepton number conservation.

    $L_{\mu }\text{:}0+0\to 0+0$

Thus, muon lepton number is conserved.

Check for tau lepton number conservation.

    $L_{\tau }\text{:}0+0\to 0+0$

Thus, tau lepton number is conserved.

Check for strangeness number conservation.

    $S:0+0\to 0+0$

Thus, strangeness is conserved.

Conclusion:

Therefore, the electron lepton number is not conserved for ${\nu }_e+\text{p}\to \text{n}+{\text{e}}^{+}$.