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Date	May 2019	Marks available	1	Reference code	19M.3.HL.TZ2.8
Level	Higher level	Paper	Paper 3	Time zone	2
Command term	Calculate	Question number	8	Adapted from	N/A

Question

A proton has a total energy 1050 MeV after being accelerated from rest through a potential difference V.

Define total energy.

[1]

Determine the momentum of the proton.

[1]

bi.

Determine the speed of the proton.

[2]

bii.

Calculate the potential difference V.

[1]

biii.

Markscheme

total energy is the sum of the rest energy and the kinetic energy ✔

«p² c² = 1050²–938² therefore» p=472«MeVc^–¹»✔

bi.

$\gamma = \frac{{1050}}{{938}} = 1.12$ ✔

$v = 0.45c$

$V = 1.35 \times {10^8}$ «ms^–1» ✔

bii.

V = 112 «MV» ✔

biii.

Examiners report

Generally well answered by most candidates. A common mistake was to define the total energy in the context of classical mechanics.

Most candidates seemed to have the right starting points but mistakes were often made in attempting to convert units. The energy-momentum equation is generally best answered using only ‘MeV’ based units.

bi.

An easy calculation, that was generally well answered.

bii.

Very few candidates realised that this question required a simple calculation using eV= KE = (γ-1)E.

biii.

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.TZ2.6b.ii:
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.
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.
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.

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

Option A: Relativity

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Markscheme

Examiners report

Syllabus sections

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