Question 23M.3.HL.TZ1.5
| Date | May 2023 | Marks available | [Maximum mark: 8] | Reference code | 23M.3.HL.TZ1.5 |
| Level | HL | Paper | 3 | Time zone | TZ1 |
| Command term | Calculate, Comment, Determine, Show that | Question number | 5 | Adapted from | N/A |
A muon is an unstable particle with a half-life of 1.56 μs as measured in the muon’s rest frame. Muons are produced in a laboratory and are all directed at a speed 0.866c towards a muon detector. The gamma factor () for this speed is 2.00. The detector, according to observers in the laboratory, is a distance D from the muon source.
According to laboratory observers .
Calculate D.
[2]
= 2.00 × 1.56 × 10−6 or 3.12 × 10−6 s ✓
D = «3.12 × 10−6 × 0.866 × 3 × 108 =» 811 m
Award [2] for BCA
Muon. Prepared students were able to distinguish between the rest frame of a muon and the rest frame of the detector, and then apply half time to these frames.
In the muon source rest frame (frame S), the detector is approaching at a speed 0.866c.
In frame S,
show that the distance travelled by the detector when it meets the muon source is 405 m.
[1]
0.866c × half life = 0.866c × 1.56 × 10−6 = « 405 m»
OR
distance travelled by detector = = = «405 m» ✓
Working must be seen.
determine the time taken for the detector to reach the muon source.
[1]
transit time = = 1.56 µs ✓
Award [1] for BCA.
Calculate, using the answers to (b)(i) and (b)(ii) the ratio in S.
[2]
transit time is one half life ✓
so ratio has to be ✓
Award [2] for BCA.
Comment on the ratios in (a) and (c).
[2]
the answers are the same ✓
count rates cannot vary from frame to frame / OWTTE ✓
Do not allow ECF from (c).
Award [2] for “count rates cannot vary” if student made a mistake OR no answer in (c) and well discussed here.