Baryons and mesons are made up of quarks and experience the four fundamental forces of nature - Leaving Cert Physics - Question 10 - 2008

The three positively charged quarks are:

1. Up quark (u)
2. Charm quark (c)
3. Top quark (t)

A baryon is composed of three quarks, while a meson is made up of one quark and one antiquark.

The quark composition of the proton is:

• Up quark (u) – 2
• Down quark (d) – 1 Thus, the proton consists of two up quarks and one down quark: $uu d$.

The net charge of the three pions emitted is zero. This is because:

1. The charged pions consist of two positively charged ( ext{u} ar{ ext{d}}) and one negatively charged (ar{ ext{u}} ext{d}) particle, which balance each other.
2. Since the total charge must be conserved in particle interactions, the sum of the charges before and after the collision remains zero.

To calculate the combined kinetic energy after the collision, we first need the total energy:

Using the energy equivalence of a pion: $E = mc^2$ For three pions, this is: $E = 3 imes (2.4842 imes 10^{-8} ext{ kg}) imes (2.9979 imes 10^{8} ext{ m/s})^2$ Calculating:

1. The individual energy is calculated: $E = 2.4842 imes 10^{-8} imes 8.9875517873681764 imes 10^{16} ext{ J}$
2. The total energy for the three pions becomes: $E_{total} = 6.5690 imes 10^{-11} ext{ J}$
3. Hence, the combined kinetic energy can be written as: $1.9375 imes 10^{-10} ext{ J}$

To find the maximum number of pions that could be created, we use the formula: $ext{Number of pions} = \frac{E_{initial}}{E_{pion}}$

1. Total initial energy before collision is: $2 imes 1 ext{ GeV} = 3.186 imes 10^{-10} ext{ J}$
2. Hence, $E_{pion} = 1.395 imes 10^{8} ext{ eV}$
3. Using conversions: $E_{pion} = 2.4842 imes 10^{-8} ext{ kg} imes (2.9979 imes 10^{8})^2$
4. The maximum number of pions that could be produced is therefore: $maximum = 3 + 11 = 14$