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Theme A — Space, Time and Motion

A.5.11 Muon Lifetime Experiment — IB Physics HL Revision Notes & Topical Questions

5 min read 8 parts Lesson 63 of 63 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
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Lesson summary

A.5.11 Muon Lifetime Experiment — IB PHYSICS HL notes: Use time dilation and length contraction to explain why cosmic-ray muons reach the Earth's surface.Muons are unstable subatomic particles about 200 times heavier than an electron.They are produced in the upper atmosphere by p…

  • That is about 21 half-lives by Newtonian physics
  • The muon half-life in Earth's frame is Δt
  • The muon frame measures L
  • Time to travel it is 2000/(0.98c)
  • Both views agree that a significant number survive
  • Sense check

Part 1 of 6Muons

1
Muons are unstable subatomic particles about 200 times heavier than an electron.
2
They are produced in the upper atmosphere by pion decays from cosmic rays.
3
Speed about 0.98c, half-life 1.6 μs (mean lifetime 2.2 μs).
4
In one half-life they travel about 470 m.

Part 2 of 6The puzzle

1
The surface is about 10 km below where muons are created.
2That is about 21 half-lives by Newtonian physics
  • That is about 21 half-lives by Newtonian physics very few muons would survive.
3
A considerable number are detected at the surface.
4
The observation is explained by time dilation or length contraction, depending on the observer.

Part 3 of 6Earth's frame: time dilation

1γ
1/√(1 − 0.982) = 5.
2The muon half-life in Earth's frame is Δt
γΔt0 = 5 × 1.6 μs = 8 μs.
3
Travel time for 10 km at 0.98c is about 33 μs.
  • That is about 4.1 half-lives (not 21), so a significant number remain.
4
The Earth observer sees the muon clock running slow.

Part 4 of 6Muon frame: length contraction

1
The distance of 10 km is a proper length in the Earth's frame.
2The muon frame measures L
L0/γ = 10 000/5 = 2000 m.
3Time to travel it is 2000/(0.98c)
6.8 μs.
  • That is about 4.3 half-lives, so again a significant number remain.
4
The muon sees the Earth's atmosphere contracted.

Part 5 of 6Interpreting the result

Interpreting the result
Both views agree that a significant number survive
  • Both views agree that a significant number survive the experiment gives evidence for time dilation and length contraction.
The Earth observer sees a longer lifetime (time dilation).
The muon observer sees a shorter distance (length contraction).
Sense check
  • Sense check you must always end with a longer time or a shorter distance for the muons to reach the surface.
Exam questions use only time dilation, length contraction and speed
Exam questions use only time dilation, length contraction and speed distance/time.

Part 6 of 6More from the specification

More from the specification
Muon decay event across reference frames
  • Muon decay event across reference frames detecting high proportions of surviving muons confirms relativistic time dilation between moving muon and stationary laboratory reference frames.
Stationary
  • Not moving.
Gradient
  • Slope of a graph line.
Reference frame
  • Coordinate system used by an observer.
Constant velocity
  • Zero acceleration.
Space-time interval
  • Invariant quantity (cΔt)2 − (Δx)2.
Relativistic speed
  • Relativistic speed a speed close to the speed of light, where Galilean velocity addition no longer gives correct results.

Key terms

TermMeaning
MuonUnstable subatomic particle about 200 times heavier than an electron.
Half-lifeTime for half of a sample of unstable particles to decay.
Time dilationMoving clocks measured as running slow.
Length contractionShortening of lengths along the motion.
Proper timeTime measured in the muon's rest frame.
Cosmic rayHigh-energy particle from space producing muons in the atmosphere.

Avoid these mistakes

1
Using the Earth-frame distance with the muon-frame lifetime.
2
Applying both time dilation and length contraction in the same frame.
3
Dividing instead of multiplying by γ for the dilated time.
4
Forgetting that proper time belongs to the muon frame.
5
Expecting no muons to reach the surface under Newtonian physics.

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