Question

What is the magnitude of the relativistic momentum of a proton with a relativistic total energy of 2.9 × 10^-10 J?

Answer 1

Relativistic momentum is given by:

P = $\gamma$mv

$\gamma$ = Lorentz factor = 1/sqrt (1 - v^2/c^2)

m = mass of proton = 1.6*10^-19

v = speed of proton

Now given that Total relativistic energy = E = 2.9*10^-10 J

Now we know that E = $\gamma$mc^2

$\gamma$ = E/mc^2 = 2.9*10^-10/(1.67*10^-27*(3*10^8)^2)

$\gamma$ = 1.9295

Now Using above values:

$\gamma$ = 1/sqrt (1 - v^2/c^2)

1 - v^2/c^2 = 1/$\gamma$^2

v = c*sqrt (1 - 1/$\gamma$^2)

v = 3*10^8*sqrt (1 - 1/1.9295^2)

v = 2.566*10^8 m/sec

Now Using these values of $\gamma$ and v, relativistic momentum will be:

P = $\gamma$*m*v

P = 1.9295*1.67*10^-27*2.566*10^8

P = 8.27*10^-19 kg-m/sec

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