Quarks in Particle Decay Equations (OCR A Level Physics): Revision Note

Balancing Quark transformation equations

• By looking at the transformation of quarks inside the protons and neutrons in beta decay it is possible to analyse the decay of specific quarks inside

Beta-minus decay

• In beta-minus decay, one of the neutrons in a nucleus is converted into a proton in a process that may be written as:

n → p + e^- + ${\overline{v}}_e$

• The neutron, n has the quark composition udd

• The proton, p has the quark composition uud

• So the beta-minus decay must involve a down quark converting to an up quark

d → u + e^- + ${\overline{v}}_e$

Balancing Charge

• The charge on the left side of the equation is -$\frac{1}{3}$e 

• The total charge on the right side is $\frac{2}{3}$e + (-1)e + 0 = -$\frac{1}{3}$e

• So, the decay equation is balanced in terms of charge

Beta-plus Decay

• In beta-plus decay a proton is converted into a neutron with the emission of a positron and an electron neutrino in a process that may be written as: 

p → n + e⁺ + v_e 

• The proton, p has the quark composition uud

• The neutron, n has the quark composition udd

• So, the beta-plus decay must involve an up quark converting to a down quark

u → d + e⁺ + v_e 

Balancing Charge

• The charge on the left side of the equation is +$\frac{2}{3}$e 

• The total charge on the right side is -$\frac{1}{3}$e + e + 0 = +$\frac{2}{3}$e

• So the decay equation is balanced in terms of charge

Charge must be conserved in any reaction or decay equation