Problem 33 - University Physics with Modern Physics

Question

BIO A nuclear chemist receives an accidental radiation dose of 5.0 Gy from slow neutrons (RBE = 4.0). What does she receive in rad, rem, and J/kg?

Step-by-Step Solution

Answer

500 rad, 2000 rem, 5.0 J/kg.

Step 1: Convert Gray to Rad

The dose in rads is calculated by converting the dose from Grays. Recall that 1 Gy = 100 rad. So, if the chemist receives a dose of 5.0 Gy, she receives:\(5.0 \, \text{Gy} \times 100 \, \frac{\text{rad}}{\text{Gy}} = 500 \, \text{rad}\)

Step 2: Calculate Dose in Rem

The dose in rems can be calculated by taking the dose in rads and multiplying by the Relative Biological Effectiveness (RBE). The formula is dose in rem = dose in rad × RBE. Therefore:\(500 \, \text{rad} \times 4.0 = 2000 \, \text{rem}\)

Step 3: Express Dose in J/kg

The dose given in Gy can also be expressed in J/kg since 1 Gy = 1 J/kg. Therefore, 5.0 Gy is:\(5.0 \, \text{Gy} = 5.0 \, \text{J/kg}\)

Key Concepts

Gray to Rad conversion

Radiation doses are often expressed in Gray (Gy) or rad, which are different units measuring the same thing: the amount of radiation absorbed by a material. To convert from Gray to rad, it's essential to remember the fundamental equivalence: 1 Gray is equal to 100 rad.
This means that if a person receives a dose of radiation in Grays, you can easily convert it to rads by multiplying by 100. For example, if a chemist receives 5.0 Gy, then they are exposed to 500 rad (since 5.0 multiplied by 100 equals 500).
Understanding this conversion is crucial in fields like nuclear medicine and radiation therapy, where precision in dosage keeps treatment safe and effective.

Relative Biological Effectiveness (RBE)

The Relative Biological Effectiveness, or RBE, is a measure used in radiobiology to compare the biological damage caused by different types of radiation. Not all radiation types impact living tissues equally; this is where RBE comes into play.
RBE considers how effective a specific type of radiation is at causing biological harm compared to a standard reference, typically X-rays or gamma rays. To calculate the dose in rem (roentgen equivalent man), which measures the biological effect of the absorbed radiation, you multiply the dose in rad by the RBE. For instance, if you have a dose of 500 rad and an RBE of 4.0 from slow neutrons, the effective dose in rem would be 2000 rem (500 rad multiplied by 4.0).
This concept is especially important in assessing radiation exposure risks in nuclear power settings, medical radiology, and radiation protection.

Radiation dose units (rad, rem, Gy)

Radiation dose units are fascinating because they indicate different aspects of radiation interactions with matter and biological tissues.
Let’s delve into three common units: rad, rem, and Gray (Gy).

• The rad (radiation absorbed dose) quantifies the amount of radiation energy absorbed per unit mass of tissue, with 1 rad equaling 0.01 Gy.
• The Gray (Gy) is an SI unit where 1 Gy equals the absorption of one joule of radiation energy per kilogram of matter, making it a more standardized unit. This can help track doses in settings like medical imaging or therapy where precision is substantial.
• The rem, or roentgen equivalent man, is used to measure the biological effects of absorbed radiation.
  It’s calculated by multiplying the rad by the RBE, reflecting the fact that different radiations have differing potential for biological damage.

These units enable professionals to evaluate and manage exposure, ensure safety, and deliver effective treatment, making them crucial in both practical and clinical contexts.