Final answer:
The dose in Sv to the chest of a patient undergoing an x-ray can be calculated by multiplying the x-ray beam intensity, area of chest exposed, and the x-ray absorption in tissue.
The resulting energy absorbed can then be divided by the exposure time to obtain the dose. This dose can be converted to Sv by multiplying it by the mass of the chest. The calculated dose in Sv is approximately 3.152 Sv, which does not match any of the given options.
Step-by-step explanation:
To calculate the dose in Sv (Sievert) to the chest, we need to first find the energy absorbed by the chest. The energy absorbed can be calculated by multiplying the x-ray beam intensity (1.50 W/m²) by the area of the chest exposed (0.0750 m²) and the x-ray absorption in tissue (35.0%).
Energy Absorbed = x-ray beam intensity × area of chest exposed × x-ray absorption in tissue
Next, we can find the dose in Sv by dividing the energy absorbed by the exposure time (0.250 s).
Dose = Energy Absorbed / Exposure Time
Plugging in the given values:
- Energy Absorbed = (1.50 W/m² × 0.0750 m² × 0.35) = 0.0394 J
- Dose = 0.0394 J / 0.250 s = 0.1576 J/s
The dose is measured in J/s, but 1 Sv is equivalent to 1 J/kg. Since we are interested in the dose to the chest (which has a mass of approximately 20 kg), we can multiply the dose by the mass of the chest to convert it to Sv.
Dose in Sv to the Chest = Dose × Mass of Chest
- Dose in Sv to the Chest = 0.1576 J/s × 20 kg = 3.152 Sv
Therefore, the dose in Sv to the chest is approximately 3.152 Sv. None of the given options match the calculated value, so none of them are correct.