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Date	May 2018	Marks available	1	Reference code	18M.3.HL.TZ2.6
Level	Higher level	Paper	Paper 3	Time zone	2
Command term	Draw	Question number	6	Adapted from	N/A

Question

Two protons, travelling in opposite directions, collide. Each has a total energy of 3.35 GeV.

As a result of the collision, the protons are annihilated and three particles, a proton, a neutron, and a pion are created. The pion has a rest mass of 140 MeV c^–2. The total energy of the emitted proton and neutron from the interaction is 6.20 GeV.

Calculate the gamma (γ) factor for one of the protons.

[1]

a.

Determine, in terms of MeV c^–1, the momentum of the pion.

[3]

b.i.

The diagram shows the paths of the incident protons together with the proton and neutron created in the interaction. On the diagram, draw the path of the pion.

[1]

b.ii.

Markscheme

γ «= $\frac{{3350}}{{938}}$ » = 3.37

[1 mark]

a.

energy of pion = (3350 × 2) – 6200 = 500 «MeV»

500² = p²c² + 140²

p = 480 «MeV c^–1»

[3 marks]

b.i.

path of pion constructed in direction around 4–5 o’clock by eye

M18/4/PHYSI/HP3/ENG/TZ2/06.b.ii/M

[1 mark]

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)

Show 27 related questions

18M.3.HL.TZ1.6b:
State the rest mass of the pion with an appropriate unit.
18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
16N.3.HL.TZ0.8a: Explain, in terms of a conservation law, why two photons need to be created.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
16N.3.HL.TZ0.8b:
Determine the speed of the incoming electron.
16N.3.HL.TZ0.8c:
Calculate the energy and the momentum for each photon after the collision.
17M.3.HL.TZ1.5a:
Calculate the potential difference V.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
19M.3.HL.TZ1.6a:
Show that energy is conserved in this decay.
19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.5a(ii):
the speed.
17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the...
20N.3.HL.TZ0.6a: Define rest mass.
17M.3.HL.TZ2.6:
A lambda $\Lambda$ ⁰ particle at rest decays into a proton p and a pion ${\pi ^ - }$ according to the reaction

$\Lambda$ ⁰ → p + $\pi$ ^–

where the rest energy of p = 938 MeV and the rest energy of $\pi$ ^– = 140 MeV.

The speed of the pion after the decay is 0.579c. For this speed $\gamma$ = 1.2265. Calculate the speed of the proton.
18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
20N.3.HL.TZ0.6b:
Calculate the total energy of the deuterium particle in $MeV$ .
19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.8biii:
Calculate the potential difference V.
17M.3.HL.TZ1.5b:
The proton collides with an antiproton moving with the same speed in the opposite direction. As a result both particles are annihilated and two photons of equal energy are produced.

Determine the momentum of one of the photons.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.

Hide related questions

Option A: Relativity » Option A: Relativity (Additional higher level option topics)

Option A: Relativity