Proton beam therapy: A beam of high-energy protons delivers a dose of 4.9×10^8 protons at a beam current of 120 nA. What is the time interval for this delivery?

• A. 6.0×10^-4 s
• B. 6.50×10^-4 s
• C. 5.0×10^-4 s
• D. 6.53×10^-4 s

Answer: (D)

Current is the rate at which charge flows, so delivering a certain number of protons means first turning those protons into total charge using the elementary charge, then dividing that charge by the beam current to get the time.

Each proton carries charge e = 1.602×10^-19 C. For N = 4.9×10^8 protons, the total charge delivered is Q = N e ≈ 4.9×10^8 × 1.602×10^-19 C ≈ 7.85×10^-11 C. The beam current is I = 120 nA = 120×10^-9 A = 1.20×10^-7 A. The delivery time is t = Q / I ≈ (7.85×10^-11 C) / (1.20×10^-7 A) ≈ 6.54×10^-4 s, which matches the given value of about 6.53×10^-4 s.