A position is created along with a electron in a cloud chamber. The position tra

Question

A position is created along with a electron in a cloud chamber. The position travels in a straight line through the chamber leaving a track 18 cm long before it encounters another electron. Both particles disappear as a result of the collision and radiation is emitted. The two events occur 0.64ns apart as measured by scientists in the lab.

a) Is the 18 cm length given a "proper length" why or why not? In the position rest frame what length of the chamber moves past the particle during the time interval between the two events?

b) In which reference frame, the lab or the rest frame of the particle, will the two events be more separated in time? Explan/show how you know?

Explanation / Answer

Firstly, this must be positron and not position.
(a) 18cm is not the Proper Time as Proper Time is the time in object's rest frame.
   according to positron lab is moving with some velocity.
now for proper length, we need to find the velocity of poristron in lab's frame i.e 18cm/.64nsec= 2.81*108 m/sec=v*;
Now from Length contraction formula :

L = L* (1-(v*/c)2)1/2   c is speed of light = 3*108m/sec.

So,proper length came out to be 51.42cm.

(b) According to results of Special Relativity: Time Dilates in observer' frame. so two events are more separated in time in the lab frame.
also called Time Dilation.

t* = t (1-(v*/c)2)1/2 .

0.64ns = t *0.350 ns.

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