Problem 32 - University Physics with Modern Physics

Question

BIO A person exposed to fast neutrons receives a radiation dose of 200 rem on part of his hand, affecting 25 g of tissue. The RBE of these neutrons is 10. (a) How many rad did he receive? (b) How many joules of energy did this person receive? (c) Suppose the person received the same rad dosage, but from beta rays with an RBE of 1.0 instead of neutrons. How many rem would he have received?

Step-by-Step Solution

Answer

(a) 20 rad, (b) 0.005 Joules, (c) 20 rem with beta rays.

Step 1: Calculate Rad from Rems

To convert rems to rads, divide the rem value by the Relative Biological Effectiveness (RBE). The formula is \( \text{Rad} = \frac{\text{Rem}}{\text{RBE}} \). Here, \( \text{Rem} = 200 \) and \( \text{RBE} = 10 \).\[ \text{Rad} = \frac{200}{10} = 20 \, \text{rad} \]

Step 2: Convert Rad to Joules

1 rad is equivalent to 0.01 joules per kilogram. To find the energy in joules (\( E \)), use the formula:\[ E = \text{Rad} \times \text{mass in kg} \times 0.01 \, \text{J/kg} \]First, convert 25 g to kg: 25 g = 0.025 kg.\[ E = 20 \, \text{rad} \times 0.025 \, \text{kg} \times 0.01 \, \text{J/kg} = 0.005 \, \text{Joules} \]

Step 3: Calculate Rem from Beta Rays Exposure

Using the same rad dosage from beta rays with RBE of 1, the rem value (biological dose) is calculated by multiplying the rad dosage by the RBE:\( \text{Rem} = \text{Rad} \times \text{RBE} \)\[ \text{Rem}_{\beta} = 20 \, \text{rad} \times 1 = 20 \, \text{rem} \]

Key Concepts

Understanding Relative Biological Effectiveness (RBE)

In radiation dose measurement, the Relative Biological Effectiveness (RBE) is a crucial concept. It helps us compare the biological damage caused by different types of radiation. RBE is essentially a measure of how much more, or less, damaging a specific type of radiation is compared to a standard, usually x-rays or gamma rays.
To put it simply, RBE adjusts the absorbed dose to reflect the biological potency of the radiation. If radiation has a high RBE, it means it's more effective at causing biological damage, even with a smaller absorbed dose. For instance, if fast neutrons have an RBE of 10, as in the given exercise, it means they are ten times more effective in causing biological damage than the reference radiation.
Understanding RBE is important:

• It helps in comparing different radiation therapies in medical treatments.
• It allows for better safety protocols in environments with radiation exposure.
• It aids in accurately assessing the risk and damage in case of accidental exposure.

RBE plays a significant role in ensuring the calculated dose reflects the actual biological impact on living tissues.

Converting Rad to Joules

Radiation doses are often expressed in units called rads. A 'rad' (Radiation Absorbed Dose) measures the amount of radiation energy absorbed per unit mass of tissue. Understanding the conversion from rads to joules is useful for quantifying the energy aspect of radiation dose.
To convert rad to joules, we use the relationship: **1 rad = 0.01 joules per kilogram**. This conversion helps determine the actual energy absorbed by the tissue. In the exercise, 25 g of tissue was exposed so this mass needs to be converted to kilograms (25 g = 0.025 kg) before using it in the formula:
\[ E = ext{Rad} \times ext{mass in kg} \times 0.01 \, ext{J/kg}\]
For example, with 20 rad absorbed, the energy in joules is:

• First convert grams to kilograms (25 g = 0.025 kg)
• Apply the formula: 20 rad \( \times 0.025 \, \text{kg} \times 0.01 \, \text{J/kg} \)
• This results in an absorbed energy of 0.005 joules.

This process highlights how a small amount of absorbed radiation can translate into an equally small energy deposit into tissue.

Examining Beta Radiation

Beta radiation is a type of radiation consisting of high-energy, high-speed electrons or positrons. Its biological effects, like other radiation types, depend significantly on its energy and the RBE value. In the context of the given problem, the RBE for beta radiation is 1.
This implies that, in terms of biological damage, 1 rad of beta radiation equals 1 rem, since its biological effectiveness is similar to reference radiation like x-rays. This characteristic of beta radiation makes it easier to handle and calculate compared to more biologically potent forms like neutrons or alpha particles.
Beta radiation is noteworthy because:

• It is commonly encountered in medical & industrial applications, and environmental radiation.
• Its lower RBE makes it less damaging per unit absorbed compared to other radiation types like neutrons.
• Its applications range from treating certain health conditions (like some cancer types) to use in lab experiments.

Understanding beta radiation, and how it differs from other types of radiation in terms of RBE, is essential for accurate radiation dose assessment, especially in scenarios where mixed radiation types are present.