10. 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 dE Sm= Ρ 144 = dx, Ep(MeV) (3) In Ep(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. Starting with formule in notes: (Eqn. [18]) S₁ = (ze²)². 41 ZNA [la (2 mo² ) - In (1- B²) -ẞ²] 411 €0 Amσ² we can re-curite it as follows: 2 S = (ze² )². 4πIZNA 471 Eo A M · [ In ( 2 mora (²) - en (1-B²) - B² ] C 28130 Using the properties of Ggarithms ތ S = (ze²)² 477 4T1ε。· Mc² or, finelly: 2 4118 ZNA. [In (2C² ) + ba (ẞ²) - In (1-B²) 1"} 471 Z2ZNA I ++ MT. 22. [P₁ (²) + (15)-B"] AB² I In this form, it is easy to see the units sall e² = 1.44 x 10-13 MeV.co 47180 3 Mc² = 0.511 Mev Crest mass of election) volewles/and electrons en molewle Z2ZNA will have units of g-1 A

10. 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 dE Sm= Ρ 144 = dx, Ep(MeV) (3) In Ep(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. Starting with formule in notes: (Eqn. [18]) S₁ = (ze²)². 41 ZNA [la (2 mo² ) - In (1- B²) -ẞ²] 411 €0 Amσ² we can re-curite it as follows: 2 S = (ze² )². 4πIZNA 471 Eo A M · [ In ( 2 mora (²) - en (1-B²) - B² ] C 28130 Using the properties of Ggarithms ތ S = (ze²)² 477 4T1ε。· Mc² or, finelly: 2 4118 ZNA. [In (2C² ) + ba (ẞ²) - In (1-B²) 1"} 471 Z2ZNA I ++ MT. 22. [P₁ (²) + (15)-B"] AB² I In this form, it is easy to see the units sall e² = 1.44 x 10-13 MeV.co 47180 3 Mc² = 0.511 Mev Crest mass of election) volewles/and electrons en molewle Z2ZNA will have units of g-1 A