Question

Problem 27.37 - New A gamma-ray photon produces an electron and a positron, each with a kinetic energy of 237 keV. h = 6.626 x 10-34 J:s, c= 2.998 x 108 m/s, me = 0.511 MeV/c?, e = 1.602 x 10-19 C. Determine the energy of the photon. Express your answer using three significant figures. V AEV O 2 ? E = Submit Request Answer Part B Determine the wavelength of the photon. Express your answer to three significant figures and include the appropriate units. GÅ * o 2 ? 1= Value Units Submit Request Answer

Please answer both Parts A and B, thanks!!

Answer 1

a) The total energy of the gamma ray is
E = 2 (rest mass energy of electron) + total kinetic energy of the electron and photon
The electron rest mass is
m_e =  0.511 MeV/c²
The electron rest mass energy is
E₀ = m_e c² = 0.511 MeV /c² x c² = 0.511 MeV
The total energy of the photon
E = 2 x 0.511 MeV + 2 x (237 keV)
E = 1.022 MeV + 474 keV
E = 1.496 MeV = 1.50 MeV
B) Using E = h c / $\lambda$
$\lambda$ = h c / E
$\lambda$ = 6.626 x 10^-34 Js x 2.998 x 10⁸ m/s /  1.496 x 10⁶ x 1.602 x 10^-19 J
$\lambda$ = 8.289 x 10^-13 m
$\lambda$ = 0.00829 Angstroms