Calculate the CSDA range win a micron of a 46 MeV alpha part

Calculate the CSDA range (w/in a micron) of a 4.6 MeV alpha particle in water. Compare this to your answer in #6 of Problem Set 3. How do the alpha and the proton (of the same energy) compare with respect to range?

Solution

CSDA range formula:

R=Int(dE/S) limits:0 to E=4.6MeV

Here: S= stopping power of alpha particle in water

Use the data in tables in our textbook to take the value of S at 4.6 MeV

substitute the values of E and S in below equation and solve for range

R=E/S

Compare alpha and proton as follows

R-alpha=(M/Z^2)R_proton

In water speed of alpha particle and the proton are the same

So the ratio between kinetic energy is

T_alpha/T_proton = M_alpha/M_proton=4

Use this information and data in the tablea in our text book and compare the results for two particles

Note: required data is missing in problem, so we can use the above relations and solve it