Question

In proton beam therapy, a beam of high-energy protons is used to kill cancerous cells in a tumor. In one system, the beam, which consists of protons with an energy of 2.8×10−11J, has a current of 84 nA. The protons in the beam mostly come to rest within the tumor. The radiologist has ordered a total dose corresponding to 3.4×10−3J of energy to be deposited in the tumor.

Answer 1

The number of protons that strike the tumor each second is $1.75 \times 10^8$ protons.

Given the following data:

• Energy of proton = $2.8 \times 10^{-11}$ Joules.

• Current = 84 nA to A = $84 \times 10^{-9}$ Ampere.

• Energy of total dose = $3.4 \times 10^{-3}$ Joules.

Scientific data:

• Charge of proton = $1.602 \times 10^{-19}$ C.

To determine the number of protons that strike the tumor each second:

How to determine the number of protons.

Mathematically, the quantity of charge per unit time is given by this formula:

$Q =It=Ne\\\\N = \frac{Q}{e}$

Where:

• N is the number of protons.

• t is the time measured in seconds.

• I is the current.

• e is the charge of protons.

Substituting the parameters into the formula, we have;

$N=\frac{2.8 \times 10^{-11} }{1.602 \times 10^{-19}} \\\\N = 1.75 \times 10^{8}$protons.

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