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Chapter 37: Q51P (page 1148)

Question: What must be the momentum of a particle with mass m so that the total energy of the particle is 3.00 times its rest energy?

Short Answer

Expert verified

Answer

The momentum of the particle is 2.83 mc.

Step by step solution

01

Relativistic momentum of a particle.

The relativistic momentum of particle is defined as

p=纬mv

Where,纬 is the Lorentz factor, mis the rest mass and v is the speed of the particle.

02

Determine Lorentz factor from the given relation.

The given relation is

E=3Eo

Here, E is the total energy and E0 is the rest mass energy.

纬mc2=3mc2纬=3

03

Determine speed of the particle from the Lorentz factor 

.

The Lorentz factor is defined in terms of speed is

纬=11-V2/C2vc=1-1纬2

Substitute the values and solve as:

vc=1-132v=0.9428c

Substitute Lorentz factor and speed of the particle in momentum expression and solve as:

p=3m0.9428c=2.83mc

Hence, the momentum of the particle is 2.83 mc .

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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脳108light-years away. The most intense light is emitted by the oxygen in NGC 7319. In a laboratory that emission is at wavelength 位=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?

Reference frame S鈥� is to pass reference frame S at speed v along the common direction of the and x axes, as in Fig. 37-9. An observer who rides along with frame S鈥� is to count off a certain time interval on his wristwatch. The corresponding time interval 鈭�t is to be measured by an observer in frame S. Figure 37-22 gives 鈭�tversus speed parameter 尾for a range of values for . The vertical axis scale is set by ta 14.0 s. What is interval 鈭�t if v = 0.98c?

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