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 80 nA. The protons in the beam mostly come to rest within the tumor. The radiologist has ordered a total dose corresponding to 3.6×10−3J of energy to be deposited in the tumor. How long should the beam be in order to deliver the required dose?

Answer 1

To calculate the time required for the beam to deliver the required dose, we use the equation Energy = Power x Time. Given the power of the beam and the desired energy, we can calculate the time required. In this case, the time required is 1.607 x 10^15 s.

Step-by-step explanation:

To calculate the time required for the beam to deliver the required dose, we can use the equation:

Energy = Power x Time

The power of the beam can be calculated using the formula:

Power = Current x Energy of each proton

Given that the energy of each proton is 2.8×10-11 J and the current is 80 nA (which is equivalent to 80 x 10-9 A), we can substitute these values into the formula:

Power = (80 x 10-9 A) x (2.8×10-11 J) = 2.24 x 10-18 J/s

Now, we can rearrange the equation to solve for time:

Time = Energy / Power

Substituting the given energy of 3.6×10-3 J and the calculated power of 2.24 x 10-18 J/s, we can find the time required:

Time = (3.6×10-3 J) / (2.24 x 10-18 J/s) = 1.607 x 1015 s