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PHYSICS, M7 2024 HSC 27

The simplified model below shows the reactants and products of a proton-antiproton reaction which produces three particles called pions, each having a different charge.

\(\text{p}+\overline{\text{p}} \rightarrow \pi^{+}+\pi^0+\pi^{-}\)

There are no other products in this process, which involves only the rearrangement of quarks. No electromagnetic radiation is produced. Assume that the initial kinetic energy of the proton and antiproton is negligible.

Protons consist of two up quarks \(\text{(u)}\) and a down quark \(\text{(d)}\) . Antiprotons consist of two up antiquarks \((\overline{\text{u}})\) and a down antiquark \((\overline{\text{d}})\). Each of the pions consists of two quarks.

The following tables provide information about hadrons and quarks.

Table 1: Hadron Information

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \quad \quad \ \ \textit{Particle} & \ \ \textit{Rest mass} \ \ & \quad \textit{Charge} \quad \\
& \left(\text{MeV/c}^2\right)&\\
\hline
\rule{0pt}{2.5ex} \text {proton (p)} \rule[-1ex]{0pt}{0pt} & 940 &  +1 \\
\hline
\rule{0pt}{2.5ex} \text {antiproton}(\overline{\text{p}}) \rule[-1ex]{0pt}{0pt} & 940 & -1  \\
\hline
\rule{0pt}{2.5ex} \text {neutral pion }\left(\pi^0\right) \rule[-1ex]{0pt}{0pt} & 140 & \text{zero} \\
\hline
\rule{0pt}{2.5ex} \text{positive pion }\left(\pi^{+}\right) \rule[-1ex]{0pt}{0pt} & 140 & +1 \\
\hline
\rule{0pt}{2.5ex}\text {negative pion }\left(\pi^{-}\right) \rule[-1ex]{0pt}{0pt} & 140 &  -1\\
\hline
\end{array}

 
Table 2: Quark charges

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \quad \quad \ \ \textit{Particle} \rule[-1ex]{0pt}{0pt} & \quad \textit{Charge} \quad \\
\hline
\rule{0pt}{2.5ex} \text {down quark (d)} \rule[-1ex]{0pt}{0pt} & -\dfrac{1}{3}  \\
\hline
\rule{0pt}{2.5ex} \text {up quark (u)} \rule[-1ex]{0pt}{0pt} & +\dfrac{2}{3}\\
\hline
\rule{0pt}{2.5ex} \text {down antiquark}(\overline{\text{d}}) \rule[-1ex]{0pt}{0pt} & +\dfrac{1}{3}\\
\hline
\rule{0pt}{2.5ex} \text{up antiquark }(\overline{\text{u}}) \rule[-1ex]{0pt}{0pt} & -\dfrac{2}{3}  \\
\hline
\end{array}

  1. Identify the quarks present in the \(\pi^{-}, \pi^{+}\)and the \(\pi^0\) particles.   (2 marks)

  2. The energy released in the reaction is shared equally between the pions.
  3. Calculate the energy released per pion in this reaction.   (2 marks)

  4. Calculation of the pions' velocities using classical physics predicts that each pion has a velocity, relative to the point at which the proton-antiproton reaction occurred, which exceeds 3 × 10\(^8\) m s\(^{-1}\).
  5. Explain the problem with this prediction and how it can be resolved.   (3 marks)

Show Answers Only

a.   \(\pi^{-}:\ \overline{\text{u}}\text{d}\)

\(\pi^{+}:\ \text{u}\overline{\text{d}}\)

\(\pi^{0}:\ \text{u}\overline{\text{d}}\)
 

b.   \(\text{Initial mass}\ = 940 + 940 =  1880\ \text{MeV/c}^{2} \)

\(\text{Final mass}\ = 3 \times 140 = 420\ \text{MeV/c}^{2} \)

\(\Delta \text{Mass (per pion)}\ = \dfrac{1460}{3} = 487\ \text{MeV/c}^{2} \)

\(\text{Using}\ \ E=mc^2:\)

\(\text{Energy released (per pion)}\ = 487\ \text{MeV}\)
 

c.   Problem with prediction:

  • The calculation shows the pions moving faster than light speed (3 × 10\(^{8}\) m/s), which can’t happen in reality.

Resolving the problem:

  • Since these pions are moving at extremely high speeds, we need to account for relativity.
  • Relativity means that pions’ mass actually increases as they get faster, which prevents them from ever reaching light speed.
  • Part of the energy given to the pions goes into increasing their mass rather than just increasing their velocity.

Show Worked Solution

a.   \(\pi^{-}:\ \overline{\text{u}}\text{d}\)

\(\pi^{+}:\ \text{u}\overline{\text{d}}\)

\(\pi^{0}:\ \text{u}\overline{\text{d}}\)
 

b.   \(\text{Initial mass}\ = 940 + 940 =  1880\ \text{MeV/c}^{2} \)

\(\text{Final mass}\ = 3 \times 140 = 420\ \text{MeV/c}^{2} \)

\(\Delta \text{Mass (per pion)}\ = \dfrac{1460}{3} = 487\ \text{MeV/c}^{2} \)

\(\text{Using}\ \ E=mc^2:\)

\(\text{Energy released (per pion)}\ = 487\ \text{MeV}\)
 

♦ Mean mark (b) 41%.

c.   Problem with prediction:

  • The calculation shows the pions moving faster than light speed (3 × 10\(^{8}\) m/s), which can’t happen in reality.

Resolving the problem:

  • Since these pions are moving at extremely high speeds, we need to account for relativity.
  • Relativity means that pions’ mass actually increases as they get faster, which prevents them from ever reaching light speed.
  • Part of the energy given to the pions goes into increasing their mass rather than just increasing their velocity.
♦ Mean mark (c) 43%.

PHYSICS, M8 EQ-Bank 13 MC

The table lists the first generation of quarks and antiquarks.

   

The Standard Model of matter states that baryons, such as protons and neutrons, consist of three quarks.

Using the table, which of the following represents the quark composition for a neutron and an antineutron, respectively?

  1. `text{u}\text{u}\text{d} and bar text{u}\bar text{u}\bar text{d}`
  2. `bar text{u}\bar text{u}\bar text {d} and text{u}\text{u}\text{d}`
  3. `text{u}\text{d}\text{d} and bar text{u}\bar text{d}\bar text{d}`
  4. `bar text{u}\bar text{d}\bar text{d} and text{u}\text{d}\text{d}`
Show Answers Only

`C`

Show Worked Solution
  • A neutron has a charge of zero, so it is made up of one up quark and two down quarks.
  • An antineutron is composed of the corresponding antiquarks. So, it is made up of one up antiquark and two down antiquarks.

`=>C`

PHYSICS, M8 2015 HSC 34e

Assess the impact of THREE advances in knowledge about particles and forces on the understanding of the atomic nucleus.   (6 marks)

Show Answers Only

Three of many possible developments are included below.

Advance One:

  • The discovery of the neutron allowed scientists to understand the masses of the nuclei.
  • This discovery enabled scientists to better identify trends in both the periodic table.

Advance Two:

  • Knowledge of the strong nuclear force helps us to explain the interaction between protons and neutrons in the nucleus, and how this force can overcome the electrostatic  force of repulsion.
  • This discovery helps to explain why certain isotopes are unstable.

Advance Three:

  • Knowledge that protons and neutrons are made from different combinations of two types of quarks.
  • This helped to unify our understanding of subatomic particles, informing our base knowledge of quantum physics through the development of the Standard Model.
Show Worked Solution

Advance One:

  • The discovery of the neutron allowed scientists to understand the masses of the nuclei.
  • This discovery enabled scientists to better identify trends in both the periodic table.

Advance Two:

  • Knowledge of the strong nuclear force helps us to explain the interaction between protons and neutrons in the nucleus, and how this force can overcome the electrostatic  force of repulsion.
  • This discovery helps to explain why certain isotopes are unstable.

Advance Three:

  • Knowledge that protons and neutrons are made from different combinations of two types of quarks.
  • This helped to unify our understanding of subatomic particles, informing our base knowledge of quantum physics through the development of the Standard Model.

♦♦♦ Mean mark 32%.

PHYSICS M8 2022 HSC 5 MC

Protons and neutrons are made up of quarks. The table shows the charges of these quarks.
 

What combination of quarks forms a neutron?

  1. 1 up, 1 down
  2. 1 up, 2 down
  3. 2 up, 1 down
  4. 2 up, 2 down
Show Answers Only

`B`

Show Worked Solution
  • Baryons such as neutrons are always are made up of three quarks.
  • Neutrons are electrically neutral and are comprised of one up quark and two down quarks.

`=>B`

PHYSICS, M8 2019 HSC 12 MC

The table shows two types of quarks and their respective charges.
 

In a particular nuclear transformation, a particle having a quark composition `udd` is transformed into a particle having a quark composition `u ud`.

What is another product of this transformation? 

  1. Electron
  2. Neutron
  3. Positron
  4. Proton
Show Answers Only

`A`

Show Worked Solution
  • The particle with quark composition `udd` is a neutron.
  • It is transformed into a particle with quark composition `udd` which is a proton.
  • To conserve charge, an electron must also be a product.

`=>A`


♦ Mean mark 51%.