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Lecture05

# Lecture05 - Lecture5 Jan.20 Rela1vityII...

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Lecture 5 Jan. 20 Rela1vity II h7p://aniketjha.blogspot.com/2010/07/emc2.html

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i‐clicker Quiz (Jan. 18) A) 0 B) me C) 2m e D) 4m e • An electron and positron with equal and opposite momenta collide head on and annihilate into 2 photons, each measured with 1.022 MeV energy. What is the invariant mass of the interac1on? m e = 0.511 MeV/c 2
3 How much energy would be required to accelerate a par1cle of mass m from rest to a speed of 0.5 c ? Express the answer as a mul1ple of the rest energy. E i = mc 2 E f = γ mc 2 Δ E = E f E i = γ 1 ( ) mc 2 γ = 1.155 Δ E = 0.155 mc 2

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4 At what value of u/c does the measured mass of a par1cle exceed its rest mass by 11 % ? γ = 1.11 = 1 1 β 2 1 β 2 = 1 1.11 = 0.9009 β 2 = 1 0.9009 ( ) 2 β = 1 0.9009 ( ) 2 = 0.434
5 How much work must be done on a proton to increase its speed from 0.1 c to 0.2 c ? (The rest energy of a proton is 938.3 MeV .) E 1 = γ 1 mc 2 E 2 = γ 2 mc 2 γ 1 = 1.0050 γ 2 = 1.0206 Δ E = γ 2 γ 1 ( ) mc 2 = Δ γ mc 2 = 0.0156 mc 2 Δ E = 14.7 eV

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6 A proton with rest energy of 938 MeV has a total energy of 1000 MeV. (a) What is the value of u/c ? (b) What is the proton's momentum? Express your answer in units of MeV/ c E = γ mc 2 = 1000 MeV γ = 1000 MeV 938 MeV = 1.0661 β = 1 1/ γ 2 = 0.3466 E 2 = pc ( ) 2 + mc 2 ( ) 2 pc ( ) 2 = E 2 mc 2 ( ) 2 = 1000

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