IB Questionbank

User interface language: English | Español

Date	May 2019	Marks available	2	Reference code	19M.3.HL.TZ1.6
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Calculate	Question number	6	Adapted from	N/A

Question

The particle omega minus ( ${\Omega ^ - }$ ) decays at rest into a neutral pion ( ${\pi ^0}$ ) and the xi baryon ( ${\Xi ^ - }$ ) according to

^{${\Omega ^ - } \to {\pi ^0} + {\Xi ^ - }$}

The pion momentum is 289.7 MeV c^–1.

The rest masses of the particles are:

${\Omega ^ - }$ : 1672 MeV c^–2

${\pi ^0}$ : 135.0 MeV c^–2

${\Xi ^ - }$ : 1321 MeV c^–2

Show that energy is conserved in this decay.

[3]

Calculate the speed of the pion.

[2]

Markscheme

momentum of xi baryon is also 289.7«MeVc⁻¹» ✔

total energy of xi baryon and pion is $\sqrt {{{289.7}^2} + {{1321}^2}} + \sqrt {{{289.7}^2} + {{135.0}^2}} = 1672$ «MeV» ✔

which equals the rest energy of the omega ✔

Allow a backwards argument, assuming the energy is equal.

$\gamma « = \frac{{\sqrt {{{289.7}^2} + {{135.0}^2}} }}{{135.0}} » = 2.367$ ✔

$v «= \sqrt {1 - \frac{1}{{{{2.367}^2}}}} c » = 0.903c$ ✔

Award [2] for bald correct answer.

Examiners report

Energy conservation in a decay. This relativistic mechanics question was very challenging. Only a few candidates were able to calculate the total energy of the baryon and pion, despite being able to recognize the correct momentum of the baryon. The same for the speed of the pion in b), most of the attempts demonstrated by candidates were not relevant.

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.
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.

Hide related questions

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

Option A: Relativity

Question

Markscheme

Examiners report

Syllabus sections

View options