Question: I need 3.835*10^18 converted to MeV/c instead of kg m/s. Original Q: W

Question

Question: I need 3.835*10^18 converted to MeV/c instead of kg m/s.

Original Q: What would be the momentum of this proton (0.992c) ? Express your answer with the appropriate units.

Credit to Cvrram for figuring out below:

If the proton is accelerated through a potenti al difference work done is equal to change in potenti al energy The rest mass of the proton is mc938MeV 1 (938Mev) (0.992c) 6490 MeV (approximately) 6490MeV (approximately) Momentum of the proton is, 1,627 x109 k (0 992c) 0.992c -(0 9920) (0.992c1 1.627 x10 k (o992(3x10 m/s) 270992 (0992(3x108 m/s)) (0.992c)? -3.835x10+kgm r 40x10-18 kg.m/s (approximately)

Explanation / Answer

3.835 x 10-18 kg m/s

1MeV = 1 million electron Volt = 106 x eV = 106 x 1.60217662 × 10-19  Joules

1MeV = 106 x 1.60217662 × 10-19  Joules = 1.60217662 x 10-13 J

Joule = Kgm2/s2

1MeV = 1.60217662 x 10-13 J = 1.60217662 x 10-13 Kgm2/s2

dividing both sides by speed of light

1MeV/c = 1.60217662 x 10-13 / (3x108) kgm/s = 5.340588733 x 10-22 kgm/s

So, 1 MeV/c = 5.340588733 x 10-22 kgm/s

1kgm/s = 1 / ( 5.340588733 x 10-22) MeV/c

1kgm/s = 1.872452739 x 1021  MeV/c

3.835 x 10-18 kgm/s = 3.835 x 10-18 x 1.872452739 x 1021  MeV/c = 7180.856253 MeV/c

Ans = 3.835 x 10-18 kgm/s = 7180.856253 MeV/c

Edit # :

The previous guy took the mass of proton as 1.627 x 10-27 kg

Actually it is 1.6726219 × 10-27    kg in which case the momentum would be

P = mv

P = 1.6726219 × 10-27 x 0.992 x 3x108 / (1 - 0.9922 )1/2  = 3.943129543 x 10-18 kg m/s

or 3.943129543 x 10-18 x 1.872452739 x 1021  = 7383.323713 MeV/c

By the way, more accurate answer to the first part is

[ 1/ (1 - 0.9922 )1/2 - 1 ] (938.28) = 6494.3548 MeV

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