Minimum energy a proton must have to penetrate

[cconradi]

Minimum energy a proton must have to penetrate...

Homework Statement

Determine the minimum energy that a proton must have to penetrate 30 cm of tissue, the approximate thickness of the human body.

Homework Equations

I used R=[(E/9.29)^1.8]1.11x10^-3 but I'm not sure if this is correct.

The Attempt at a Solution

R=[(E/9.29)^1.8]1.11x10^-3
30 cm=3 mm

3mm=[(E/9.29)^1.8]1.11x10^-3, then I divided by 1.11x10^-3 to get 27027.70mm=(E/9.29)^1.8
Then I took a root to the 1.8 power and got 80.64mm=E/9.29
I then multiplied by 9.29 to get 749 mEV.

Seems a bit high. Wasn't sure about units or if I even used the correct formula?
Thanks for your help!

 

[KataKoniK]

Your attempt at solving this problem is on the right track, but there are a few errors that need to be corrected.

Firstly, the formula you used is not the correct one for determining the minimum energy needed for a proton to penetrate a certain thickness of tissue. The correct formula is R=0.01E^{1.8}, where R is the range of the proton in tissue in centimeters and E is the energy of the proton in MeV. This formula is derived from the Bethe-Bloch equation, which describes the energy loss of a charged particle in a material.

Secondly, when you converted the thickness of 30 cm to millimeters, you made a mistake. 30 cm is equal to 300 mm, not 3 mm. This mistake caused your final answer to be much too high.

Lastly, when you took the root to the 1.8 power, you should have gotten R^{1/1.8}=E, not R^{1.8}=E. This is a minor error, but it will affect your final answer.

So, to solve this problem correctly, we can follow these steps:

1. Convert the thickness of 30 cm to millimeters. This gives us 300 mm.

2. Plug this value into the formula R=0.01E^{1.8} and solve for E:

300 mm=0.01E^{1.8}
Divide both sides by 0.01:
30000= E^{1.8}
Take the root to the 1.8 power:
(30000)^{1/1.8}=E
E= 171.34 MeV.

So, the minimum energy a proton must have to penetrate 30 cm of tissue is 171.34 MeV. I hope this helps! Let me know if you have any further questions.