The total energy of a proton passing through a laboratory apparatus is 10.611-nJ. What is its speed parameter β ? Use the proton mass given in Appendix B under “Best Value,” not the commonly remembered rounded number.

Short Answer

Expert verified

The speed parameter is 0.9898856096c

Step by step solution

01

Relativistic Total energy

The total energy of an object is the sum of its rest mass energy, kinetic energy if its moving, and potential energy if it is under some force.The total relativistic energy of an object moving at constant velocity will be expressed as

E=γmc2

Where, γis the Lorentz factor, and m, is the rest mass of the object. Here in the question, it is asked to use the best value for the proton’s mass1.672621637×10-27kg.

Inserting these values in the above equation to getγ,

10.611×10-9J=γ1.672621637×10-27kg3×108m/s210.611×10-9J=γ1.505359473×10-11kgm2/s2γ=10.611×10-91.505359473×10-117.048814712

02

Lorentz factor

The result of 2nd postulate of the special theory of relativity is that the clocks run slower for a moving object when measured from a rest frame. The factor by which the clock is running differently is called the Lorentz factor.

The expression for Lorentz factor is

γ=11-β2

Here βis the speed parameterv/c. Inserting the value of the Lorentz factor in this expression

γ=11-β2β=1-1γ2=1-17.0488147122=0.9898856096

The speed parameter thus obtained up to 10 significant values because the best value of proton’s mass is given in 10 significant values is asked to be considered.

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Most popular questions from this chapter

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?

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