A positive kaon (K+) has a rest mass of 494 MeV/c² , whereas a proton has a rest mass of 938 MeV/c². If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly:. A. 0.25c
B. 0.40c
C. 0.55c
D. 0.70c
E. 0.85c

0.85c

Explanation:

Rest mass of Kaon = 494 MeV/c²

Rest mass of proton  = 938 MeV/c²

The rest energy is gotten by multiplying the rest mass by the square of the speed of light c²

for the kaon, rest energy = 494c² MeV

for the proton, rest energy = 938c² MeV

Recall that the rest energy, and the total energy are related by..

= γ

which can be written in this case as

= γ ...... equ 1

where = total energy of the kaon, and

= rest energy of the kaon

γ = relativistic factor =

where

But, it is stated that the total energy of the kaon is equal to the rest mass of the proton or its equivalent rest energy, therefore...

=  ......equ 2

where is the total energy of the kaon, and

is the rest energy of the proton.

From = = 938c²    

equ 1 becomes

938c² = γ494c²

γ = 938c²/494c² = 1.89

γ = = 1.89

1.89 = 1

squaring both sides, we get

3.57( 1 - ) = 1

3.57 - 3.57 = 1

2.57 = 3.57

= 2.57/3.57 = 0.72

= 0.85

but,

v/c = 0.85

v = 0.85c

it is called kinetic energy