Question

In proton-beam therapy, a high-energy beam of protons is fired at a tumor. The protons come to rest in the tumor, depositing their kinetic energy and breaking apart the tumor

Answer 1

Part a)

Since the protons are accelerated from rest through a potential difference of 23 MV, that means that each proton will have 23 MeV of energy. That is because an electron volt is defined as the energy gained by a single unit charge going through a potential difference of one volt. And a proton has a single unit of electrical charge, meaning that it will gain 1 electron volt of energy for every volt of potential difference that it goes through.

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Part b)

Step 1) To find out how many ptons must be fired at the tumor to deliver the required amount of energy, first convert the energy of the proton from electron volts to joules:

So each proton delivers 3.68x10^-12 J.

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Step 2) Write the equation relating the total energy needed E_T, to the number n of protons of energy E_p:

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Step 3) Solve for the number of protons n:

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Step 4) Substitute in 0.20 J for the total energy needed E_T, and 3.68x10^-12 J for the proton energy E_p:

So about 5.4x10¹⁰ protons are needed to deliver the required energy.

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Part c)

Step 1) To find the total charge that is delivered to the tumor from the protons, make an equation relating the total charge Q to the number n of protons of charge q:

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Step 2) Substitute in the 5.43x10¹⁰ that was just found for the number of protons n, and 1.6x10^-19 C for the charge on a single proton q:

So about 8.7x10^-9 C are delivered to the tumor at the same time as the energy is.