Q- a positron emerges normally from a 4-mm thick slab of plastic (density= 1.14g/cm^3) with an energy of 1.62 MeV. What is the energy of the particle when it entered the slab?
Range when 0< T <= 2.5 MeV: R= .412+T^[1.27-.0954*ln(T)] where T is kinetic energy of beta particle
also ln(T)= 6.63-3.24[3.29-ln(R)]^.5
The Attempt at a Solution
Ok I know initial slab is 4mm or .4 cm and has a density of 1.14 g/cm^3. thus it has a range of .456 g/cm^2
now the range of the beta particle after it left the slab with E= 1.62 MeV is:
R= .412*1.62^[1.27 - .0954*ln(1.62)]= .744
now range total is just: R_total = .456 + .744 = 1.2
now we can solve what the initial T was going into the slab via:
ln(T) = 6.63-3.24[3.29-ln(1.2)]^.5= .9183
thus T= e^(.9183) = 2.5 MeV
However I should be getting 2.2 MeV. Does anyone see where I am going wrong?