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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 37-18 shows two clocks in stationary frame S(they are synchronized in that frame) and one clock in moving frame S'.Clocks C1and C'1read zero when they pass each other. When clocks C1and C2pass each other, (a) which clock has the smaller reading and (b) which clock measures a proper time?

How much work is needed to accelerate a proton from a speed of 0.9850c to a speed of 0.9860c?

A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a frequency (measured in the spaceship frame) of 100 MHz. To what frequency must Earth receivers be tuned to receive the report?

In Fig. 37-26a, particle P is to move parallel to the x and x' axes of reference frames S and S' , at a certain velocity relative to frame S. Frame S'" width="9">x axis of frame S at velocity v. Figure 37-26b gives the velocity localid="1664359069513" u'of the particle relative to frame localid="1664359072841" S' for a range of values for v. The vertical axis scale is set by ua'=0.800c. What value willu' have if (a)v=0.90c and (b) v→c?
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