Chapter 28, Problem 54PE

### 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

# Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of 6.80 × 10 − 27 kg and is given 5.00 MeV of kinetic energy, what is its velocity?

To determine

The velocity of helium nucleus.

Explanation

Given data:

Relativistic Kinetic energy is K.E=5.00â€‰MeV.

Mass is m=6.80Ã—10âˆ’27â€‰kg.

Formula used:

The Lorentz factor is,

â€ƒâ€ƒÎ³=11âˆ’v2c2

Rewrite the above equation for v.

â€ƒâ€ƒv=c(1âˆ’1Î³2)â€ƒâ€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.Erel+mc2mc2=K

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