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Chapter 37: Q79P (page 1151)

What is the momentum in MeV/c of an electron with a kinetic energy of 2.00MeV ?

Short Answer

Expert verified

The momentum of the electron is 2.46MeV/c.

Step by step solution

01

Lorentz factor:

The result of the postulate of special relativity is that the clock runs slower for a moving object when measured from a rest frame. The factor by which the clocks run differently is called the Lorentz factor.

The relativistic kinetic energy relation is given by

K=mec2γ-1

Here me is the electron’s rest mass, and γ is the Lorentz factor.

Using this relation to determine the Lorentz factor,

γ=Kmec2+1=2.00×106×1.6×10-19J9.1×10-31kg3×108m/s2+1=3.91+1=4.91

The Lorentz factor is expressed in terms of speed parameter β=v/c as,

γ=11-β2β=1-1γ2=1-14.912=0.979

Hence, the electron is traveling at a speed,

v=βc=0.979c

02

Relativistic Momentum:

The expression for relativistic momentum is given by

p=γmev=γβmec=γβmec2c

The rest mass energy mec2 of the electron is 0.511MeV (Table 37-3).

p=γβcmec2=4.910.979c0.511MeV=2.46MeV/c

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Most popular questions from this chapter

Figure 37-27 is a graph of intensity versus wavelength for light reaching Earth from galaxy NGC 7319, which is about 3×108light-years away. The most intense light is emitted by the oxygen in NGC 7319. In a laboratory that emission is at wavelength λ=513nm, but in the light from NGC 7319 it has been shifted to 525 nm due to the Doppler effect (all the emissions from NGC 7319 have been shifted). (a) What is the radial speed of NGC 7319 relative to Earth? (b) Is the relative motion toward or away from our planet?

Figure 37-20 shows the triangle of Fig 37-14 for six particles; the slanted lines 2 and 4 have the same length. Rank the particles according to (a) mass, (b) momentum magnitude, and (c) Lorentz factor, greatest first. (d) Identify which two particles have the same total energy. (e) Rank the three lowest-mass particles according to kinetic energy, greatest first.

An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c. What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?

A rod is to move at constant speedvalong thexaxis of reference frame S, with the rod’s length parallel to that axis. An observer in frame Sis to measure the lengthLof the rod. Which of the curves in Fig. 37-15 best gives length L(vertical axis of the graph) versus speed parameterβ?

The length of a spaceship is measured to be exactly half its rest length. (a) To three significant figures, what is the speed parameter βof the spaceship relative to the observer’s frame? (b) By what factor do the spaceship’s clocks run slow relative to clocks in the observer’s frame?
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