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Show that for the case of incident protons, in the non-relativistic limit, Bethe-Bloch's equation for the mass stopping power can be written in a more practical form as: 1 Sm= (-) 144 E(MeV) In E(eV) 459 (eV) where Sm is the mass stopping power (measured in MeV cm² g-1) and Ep is the kinetic energy of the proton. Using this formula, calculate the mass stopping power for protons of energies 1 MeV, 10 MeV and 104 MeV when the stopping medium is aluminium (Z = 13; A = 26.98; /= 150 eV). How do these calculated values compare with the experimental results shown in the figure below? Explain any observed major discrepancies. 1000 Mass stopping power S (MeV cm² g¹) 100 10 172 33.8 1.8 1 10-3 10-2 10-1 10° 10¹ 10² 103 104 Energy (MeV)
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Transcribed Image Text:Show that for the case of incident protons, in the non-relativistic limit, Bethe-Bloch's equation for the mass stopping power can be written in a more practical form as: 1 Sm= (-) 144 E(MeV) In E(eV) 459 (eV) where Sm is the mass stopping power (measured in MeV cm² g-1) and Ep is the kinetic energy of the proton. Using this formula, calculate the mass stopping power for protons of energies 1 MeV, 10 MeV and 104 MeV when the stopping medium is aluminium (Z = 13; A = 26.98; /= 150 eV). How do these calculated values compare with the experimental results shown in the figure below? Explain any observed major discrepancies. 1000 Mass stopping power S (MeV cm² g¹) 100 10 172 33.8 1.8 1 10-3 10-2 10-1 10° 10¹ 10² 103 104 Energy (MeV)
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