3) An electronand a positron both of rest energy 0.511 MeV slowly drift together

Question

3) An electronand a positron both of rest energy 0.511 MeV slowly drift togetherand annihilate into two gamma ray photons. What is the wavelengthof each of the photons? (h = 6.63 ´10-34 J×s, c = 3.00 ´108 m/s, and 1 eV = 1.60 ´10-19 J)

      a. 1.21 ´10-12 m   b. 2.43 ´10-12 m   c. 4.86 ´10-12 m   d. 9.72 ´10-12 m

4) A proton (mass = 1.67 ´10-27 kg) has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%, what isthe minimum uncertainty in its position? (h = 6.63 ´10-34 J×s, 1 eV = 1.6 ´10-19 J)

a. 9.08´ 10-13 m   b. 2.28 ´10-13 m   c. 9.08 ´10-14 m   d. 5.64 ´10-14 m

Explanation / Answer

The energy of each gamma ray photon is E =0.511 MeV                                                                  = (0.511)(1.6*10-13J) = 0.8176*10-13J We know the energy of the photon is E = hc/                                                            = hc/E                                                              = (6.63*10-34J.s)(3.0*108m/s) /(0.8176*10-13J)                                                              = 2.43*10-12m

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