What is the speed of a proton if its mass is twice its rest mass? A) 0.50c B) 0.

Question

What is the speed of a proton if its mass is twice its rest mass? A) 0.50c B) 0.68c C) 0.73c D) 0.87c E) 0.92c F) None of these What is the minimum wavelength for a gamma-ray photon to create an electron a) 1.02 times 10^-12 m b) 3.91 times 10^-9 m c) 5.36 times 10^-12 m d) 2.92 times 10^-9 m e) 1.21 times 10^-12 m f) 7.81 times 10^-10 m An anti-electron travels at a speed of 2.70c. Calculate its kinetic energy. a) 0.66 MeV b) 9.3 MeV c) 0.15 MeV d) 33 MeV e) 86 MeV f) 52 MeV g) 48 MeV h) 91 MeV i) 77 MeV j) 86 MeV k) 3.6 MeV l) 0.46 MeV m) None of the above

Explanation / Answer

11)

m = mo/sqrt(1 - v^2/c^2)

So, for m =2*mo

2*mo = mo/sqrt(1 - v^2/c^2)

So, 1 - v^2/c^2 = 1/4

So, v^2/c^2 = 3/4

So, v = sqrt(3)*c/2 = 0.87*c <--------answer

13)

KE = 0.5*mv^2

m = mo/sqrt(1 - v^2/c^2)

So, KE = 0.5*(9.11*10^-31)/sqrt(1 - (2.7/3)^2)(2.7*c)^2

= 0.5*(9.11*10^-31/sqrt(1 - (2.7/3)^2))*(2.7*10^8)^2

= 7.61*10^-14 J

= 7.61*10^-14/(1.6*10^-19*10^6)

= 0.476 MeV

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