Hadrons (AQA A Level Physics): Revision Note

The baryon Δ⁺⁺ was discovered in a particle accelerator using accelerated positive pions on hydrogen targets. Which of the following is the quark combination of this particle?

A. $\mathrm{uuu}$

B. $\mathrm{cd}\overline{\mathrm{s}}$

C. $\overline{\mathrm{u}}\mathrm{d}$

D. $\overline{\mathrm{c}}\overline{\mathrm{c}}\overline{\mathrm{c}}$

[1]

Answer:

• Since Δ⁺⁺ is a baryon, it is made up of three quarks

  • This means it is not C

• Baryons are made up of three quarks or anti-baryons are made up of three anti-quarks

  • This means it is not B (combination of two quarks and one anti-quark)

• The Δ⁺⁺ baryon has a charge of +2

• Adding up the charges of the quarks in A and D:

  • $\mathrm{uuu}=+\frac{2}{3}+\frac{2}{3}+\frac{2}{3}=+2$

  • $\overline{\mathrm{c}}\overline{\mathrm{c}}\overline{\mathrm{c}}=-\frac{2}{3}-\frac{2}{3}-\frac{2}{3}=-2$

• The quark combination of Δ⁺⁺ must therefore be $\mathrm{uuu}$

• Therefore, the correct answer is option A [1 mark]

Remembering quark combinations is useful for the exam.

However, as long as you can remember the charges for each quark, it is easy to figure out the combination by making sure the combination of quarks adds up to the total charge of the particle (just like in the worked example).