A LevelPhysicsCambridge (CIE)Revision Notes11. Particle PhysicsFundamental ParticlesThe Quark Model of Beta Decay

The Quark Model of Beta Decay (Cambridge (CIE) A Level Physics): Revision Note

Exam code: 9702

Written by: Leander Oates

Updated on 24 December 2024

Quark composition: β– & β+ decay

Beta decay happens via the weak interaction
- This is one of the four fundamental forces and it’s responsible for radioactive decays

Quark composition: β^- decay

Recall that β^- decay is when a neutron turns into a proton emitting an electron and anti-electron neutrino
More specifically, a neutron turns into a proton because a down quark turns into an up quark

Beta minus decay

Beta minus decay is when a down quark turns into an up quark

Quark composition: β⁺ decay

Recall that β⁺ decay is when a proton turns into a neutron emitting an positron and an electron neutrino
More specifically, a proton turns into a neutron because an up quark turns into a down quark

Beta plus decay

Beta minus decay is when an up quark turns into a down quark

Worked Example

The equation for β^– decay is

$n \to p + e^{-} + \bar{v_{e}}$

Using the quark model of beta decay, prove that the charge is conserved in this equation.

Answer:

Step 1: Recall the process of beta minus decay

β− decay is when a down quark changes to an up quark
- This changes a neutron into a proton

Step 2: Determine the charge on the left hand side of the equation

The quark composition of a neutron is $udd$
Adding the quark charges gives:

$+ \frac{2}{3} - \frac{1}{3} - \frac{1}{3} = + 0$

The left side of the equation has a charge of 0

Step 3: Determine the charge on the right hand side of the equation

The quark composition of a proton is $uud$
Adding up the quark charges gives:

$+ \frac{2}{3} + \frac{2}{3} - \frac{1}{3} = + 1$

The electron has a charge of −1
The anti-neutrino has a charge of 0
- Therefore, the right hand side of the equation has a charge of:

$+ 1 - 1 + 0 = 0$

Step 4: Prove that the charge is conserved

Since charge is equal on both sides, charge is conserved in the beta decay equation

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