College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.

(a)

To determine

The velocity of electron.

Explanation

Given data:

Relativistic Kinetic energyis K.Erel=0.750â€‰MeV .

Mass is m=9.11Ã—10âˆ’31â€‰kg .

Velocity of light is c=3Ã—108â€‰m/s

Formula used:

The Lorentz factor is,

â€ƒâ€ƒÎ³=11âˆ’ v 2 c 2

Rewrite the above equation for v .

â€ƒâ€ƒv=c(1âˆ’1 Î³ 2 )â€ƒâ€ƒâ€ƒ....... (1)

The relativistic kinetic energy is,

â€ƒâ€ƒK.Erel=(Î³âˆ’1)mc2

Rewrite the above equation for Î³ .

â€ƒâ€ƒK.Erel+mc2=Î³mc2Î³=K

(b)

To determine

The high velocity is consistent with kinetic energy as comapare to the rest mass energy of electron.

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