2024HSCShort answer

Q26

3 marks

Question

Muons are unstable particles produced when cosmic rays strike atoms high in the atmosphere. The muons travel downward, perpendicular to Earth’s surface, at almost the speed of light.

Classical physics predicts that these muons will decay before they have time to reach Earth’s surface.

Explain qualitatively why these muons can reach Earth’s surface, regardless of whether their motion is considered from either the muon’s frame of reference or the Earth’s frame of reference.

Try the question before revealing the answer.

Solution

Criteria	Marks
Explains why muons reach the Earth’s surface with reference to relativistic effects in both frames of reference	3
Outlines some relativistic effects that apply to the muon OR explains one relativistic effect that applies to the muon	2
Provides some relevant information	1

Sample answer: In the muon’s reference frame, the distance travelled is less than that observed by a stationery observer on Earth’s surface, due the effects of length contraction. This shortened distance means that they will get further than would be expected by an observer observing the rest length.

From the Earth’s frame of reference, the time dilation means that the half-life of the muon is dilated compared to the half-life measured in the rest frame of the muon. This greater time allows more muons to reach the ground than would otherwise be expected.

Supplied marking guidance · human reviewed

Compare this with your working, not only your final sentence.

Syllabus alignment

Module 7 · The Nature of Light

Light and Special RelativityEvaluate evidence for Einstein's postulates and analyse time dilation and length contraction.

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