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Date May 2016 Marks available 1 Reference code 16M.3.SL.TZ0.5
Level Standard level Paper Paper 3 Time zone Time zone 0
Command term Outline Question number 5 Adapted from N/A

Question

An electron is emitted from a nucleus with a speed of 0.975c as observed in a laboratory. The electron is detected at a distance of 0.800m from the emitting nucleus as measured in the laboratory.

For the reference frame of the electron, calculate the distance travelled by the detector.

[2]
a.

For the reference frame of the laboratory, calculate the time taken for the electron to reach the detector after its emission from the nucleus.

[2]
b.

For the reference frame of the electron, calculate the time between its emission at the nucleus and its detection.

[2]
c.

Outline why the answer to (c) represents a proper time interval.

[1]
d.

Markscheme

γ=4.503

\( \ll \frac{{0.800}}{{4.50}} =  \gg 0.178{\rm{m}}\)

a.

\({\rm{time}} = \frac{{0.800}}{{2.94 \times {{10}^8}}}\)

2.74 ns

b.

\(\frac{{2.74}}{{4.5}}\) OR \(\frac{{0.178}}{{2.94 \times {{10}^8}}}\)

0.608 ns

c.

it is measured in the frame of reference in which both events occur at the same position
OR
it is the shortest time interval possible

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.2 – Lorentz transformations
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