Three reaction rows show why charge, baryon number, and lepton families must all close.

Three reaction rows show why charge, baryon number, and lepton families must all close. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Muon decay closes both family ledgers

The accepted muon row keeps scaled charge -3, electron-family total 0, and muon-family total 1 on both sides.

−301⇒1-3\quad0\quad1\Rightarrow1
Muon decay ledgerLepton-family ledgers close separately.muonelectronanti-nu_enu_muQ3=-3B3=0Le=0Lmu=1Q3=-3B3=0Le=1Lmu=0Q3=0B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=1accepted

Electron to photons fails lepton number

The electron row starts with scaled charge -3 and electron-family number 1, while two photons total 0 and 0.

−3≠01≠0-3\ne0\quad1\ne0
Rejected particle ledgerThe visible status is rejected because ledgers do not close.electronphotonphotonQ3=-3B3=0Le=1Lmu=0Q3=0B3=0Le=0Lmu=0Q3=0B3=0Le=0Lmu=0rejected

Proton decay closes charge but not baryon number

The proton row keeps scaled charge 3 on both sides, but scaled baryon number changes from 3 to 0.

3=33≠03=3\quad3\ne0
Baryon rejectionCharge closes while another ledger rejects the reaction.positronphotonuudQ3=3B3=3Q3=3B3=0Le=-1Lmu=0Q3=0B3=0Le=0Lmu=0rejected