Key Stage 5
Meaning
The law of conservation of Lepton Number is the observation that in all fundamental interactions the sum of Leptons and Anti-leptons is the same before and after the interaction.
About Conservation of Lepton Number
- Leptons have a Lepton number of 1.
- Anti-leptons have a lepton number of -1.
- If a Lepton comes into existence an Anti-lepton must also come into existence.
- Conservation of Lepton Number can be applied to all fundamental interactions to balance the equations and to ascertain the types of particles produced. However, leptons do not interact via the Strong Nuclear Interaction, so while the conservation law applies, it is irrelevant.
Examples
\(p+\bar\nu_e\rightarrow n + \beta^+\)
|
|
\(p\)
|
\(+\)
|
\(\bar\nu_e\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\beta^+\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n+\nu_e\rightarrow p + \beta^-\)
|
|
\(n\)
|
\(+\)
|
\(\nu_e\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\beta^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p+\bar\nu_{\mu}\rightarrow n + \mu^+\)
|
|
\(p\)
|
\(+\)
|
\(\bar\nu_{\mu}\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\mu^+\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n+\nu_{\mu}\rightarrow p + \mu^-\)
|
|
\(n\)
|
\(+\)
|
\(\nu_{\mu}\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\mu^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p + e^- \rightarrow n + \nu_e\)
|
|
\(p\)
|
\(+\)
|
\(e^-\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\nu_e\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p + \pi^- \rightarrow K^+ + \Sigma^-\)
|
|
\(p\)
|
\(+\)
|
\(\pi^-\)
|
\(\rightarrow\)
|
\(K^+\)
|
\(+\)
|
\(\Sigma^-\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(n + \pi^- \rightarrow K^0 + \Sigma^-\)
|
|
\(n\)
|
\(+\)
|
\(\pi^-\)
|
\(\rightarrow\)
|
\(K^0\)
|
\(+\)
|
\(\Sigma^-\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(n + \pi^+ \rightarrow K^+ + \Sigma^0\)
|
|
\(n\)
|
\(+\)
|
\(\pi^+\)
|
\(\rightarrow\)
|
\(K^+\)
|
\(+\)
|
\(\Sigma^0\)
|
| Charge
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(p + \bar p \rightarrow \pi^+ + \pi^-\)
|
|
\(p\)
|
\(+\)
|
\(\bar p\)
|
\(\rightarrow\)
|
\(\pi^+\)
|
\(+\)
|
\(\pi^-\)
|
| Charge
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Baryon Number
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Strangeness
|
\(0\)
|
\(+\)
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(p\rightarrow n + \beta^+ + \nu_e\)
|
|
\(p\)
|
\(\rightarrow\)
|
\(n\)
|
\(+\)
|
\(\beta^+\)
|
\(+\)
|
\(\nu_e\)
|
| Charge
|
\(+1\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(n\rightarrow p + \beta^- + \bar\nu_e\)
|
|
\(n\)
|
\(\rightarrow\)
|
\(p\)
|
\(+\)
|
\(\beta^-\)
|
\(+\)
|
\(\bar\nu_e\)
|
| Charge
|
\(0\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(\mu^+ \rightarrow e^+ + \bar\nu_{\mu}+\nu_{e}\)
|
|
\(\mu^+\)
|
\(\rightarrow\)
|
\(e^+\)
|
\(+\)
|
\(\bar\nu_{\mu}\)
|
\(+\)
|
\(\nu_{e}\)
|
| Charge
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(-1\)
|
\(=\)
|
\(-1\)
|
\(+\)
|
\(-1\)
|
\(+\)
|
\(+1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(\mu^- \rightarrow e^- + \nu_{\mu}+\bar\nu_{e}\)
|
|
\(\mu^-\)
|
\(\rightarrow\)
|
\(e^-\)
|
\(+\)
|
\(\nu_{\mu}\)
|
\(+\)
|
\(\bar\nu_{e}\)
|
| Charge
|
\(-1\)
|
\(=\)
|
\(-1\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Baryon Number
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|
| Lepton Number
|
\(+1\)
|
\(=\)
|
\(+1\)
|
\(+\)
|
\(+1\)
|
\(+\)
|
\(-1\)
|
| Strangeness
|
\(0\)
|
\(=\)
|
\(0\)
|
\(+\)
|
\(0\)
|
\(+\)
|
\(0\)
|