Leptons (AQA A Level Physics): Revision Note

Identify all of the anti-leptons in the following decay equation.

${\mathrm{\pi }}^{+}\to {\mathrm{\mu }}^{+}+{\nu }_{\mu }$

[1]

Answer:

• ${\mathrm{\pi }}^{+}$ is a meson (type of hadron) and is made up of quarks

  • This means it is not a fundamental particle and hence not a lepton

• ${\nu }_{\mu }$ is a lepton, not an anti-lepton

• ${\mathrm{\mu }}^{+}$ is the anti-particle of the muon, and therefore it is an anti-lepton [1 mark]

If the lepton number is conserved in the following decay, identify whether particle X should be a neutrino or anti-neutrino.

$\mathrm{n}+{\mathrm{\mu }}^{+}\to \mathrm{p}+\mathrm{X}$

[1]

Answer:

Step 1: Determine the lepton number of all the particles on both sides of the equation

$0+\left(-1\right)=0+\mathrm{X}$

Step 2: Identify the lepton number of X

• If the lepton number must be conserved, X must also have a lepton number of –1

Step 3: State the particle X

• Therefore, particle X is an anti-neutrino [1 mark]

No need to fret about memorising all the different lepton numbers - the lepton number of each lepton and anti–lepton is provided on the datasheet. Remember that although quarks are fundamental particles, they have a lepton number of 0 and are classed as baryons.

Show that muon decay satisfies all the conservation laws.

[3]

Answer:

Step 1: Write out the equation for muon decay

${\mathrm{\mu }}^{-}\to {\mathrm{e}}^{-}+{\overline{\nu }}_e+{\nu }_{\mu }$

Step 2: List the quantities which must be conserved in this interaction 

• Charge, q

  • q = –1 for electrons and muons, q = 0 for neutrinos

• Electron lepton number, L_e

  • L_e = +1 for electrons, L_e = –1 for anti-electron neutrinos, L_e = 0 for muons and muon neutrinos

• Muon lepton number, L_μ

  • L_μ = +1 for muons and muon neutrinos, L_μ = 0 for electrons and electron neutrinos

Step 3: Determine if each quantity balances on each side of the equation

• Charge, q:

  • ${\mathrm{\mu }}^{-}\to {\mathrm{e}}^{-}+{\overline{\nu }}_e+{\nu }_{\mu }$

  • $\left(-1\right)=\left(-1\right)+0+0$ ✓ conserved [1 mark]

• Electron lepton number, L_e:

  • ${\mathrm{\mu }}^{-}\to {\mathrm{e}}^{-}+{\overline{\nu }}_e+{\nu }_{\mu }$

  • $0=\left(+1\right)+\left(-1\right)+0$ ✓ conserved [1 mark]

• Muon lepton number, L_μ:

  • ${\mathrm{\mu }}^{-}\to {\mathrm{e}}^{-}+{\overline{\nu }}_e+{\nu }_{\mu }$

  • $\left(+1\right)=0+0+\left(+1\right)$ ✓ conserved [1 mark]

Step 4: Write a conclusion

• The numbers on each side of the equation are equal for charge, electron lepton number and muon lepton number, therefore, muon decay satisfies these conservation laws