DP Physics (last assessment 2024)

Question 23M.3.HL.TZ2.6

Date	May 2023	Marks available	[Maximum mark: 5]	Reference code	23M.3.HL.TZ2.6
Level	HL	Paper	3	Time zone	TZ2
Command term	Calculate, Show that, State	Question number	6	Adapted from	N/A

[Maximum mark: 5]

23M.3.HL.TZ2.6

In the laboratory frame of reference, a kaon decays spontaneously into a positive pion and a negative pion that then move in opposite directions.

K⁰ → $π$ ⁺ + $π$ ⁻

The rest mass of both the pions is 140 MeV c⁻². The $π$ ⁺ has a momentum of magnitude 340 MeV c⁻¹ and the $π$ ⁻ has momentum of magnitude 113 MeV c⁻¹.

(a)

State the magnitude of the momentum of the K⁰ the instant before it decays.

[1]

Markscheme

227 «MeV c⁻¹»

(b)

Show that the energy of the $π$ ⁺ is approximately 370 MeV .

[1]

Markscheme

$E_{π^{+}} = \sqrt{140^{2} + 340^{2}}$

= 368 «MeV»

Award [1] for correct substitution or value determined to 3 SF

(c)

Calculate the rest energy of the K⁰.

[3]

Markscheme

E Pion minus = root of (140² + 113²) = «180 MeV» ✓

Rest Energy of K⁰ = $\sqrt{{(360 + 180)}^{2} - {(340 - 113)}^{2}}$ ✓

= 499 «MeV» ✓

Award [3] for BCA

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Additional higher level (AHL)

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics

Question 23M.3.HL.TZ2.6

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