A 50 kg laboratory worker is exposed to 20 mJ of beta radiation. What is the dose equivalent in mrem?

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Understand the problem: The dose equivalent in mrem is calculated using the formula: \( H = D \cdot Q \), where \( H \) is the dose equivalent, \( D \) is the absorbed dose in rad, and \( Q \) is the quality factor for the type of radiation. Beta radiation typically has a quality factor \( Q = 1 \).

Convert the absorbed dose from energy (mJ) to rad. First, recall that 1 rad = 0.01 J/kg. The absorbed dose \( D \) can be calculated using \( D = \frac{E}{m} \), where \( E \) is the energy absorbed (in joules) and \( m \) is the mass of the worker (in kilograms).

Convert the given energy from millijoules to joules: \( 20 \ \text{mJ} = 20 \times 10^{-3} \ \text{J} \).

Substitute the values into the formula for \( D \): \( D = \frac{20 \times 10^{-3}}{50} \). This will give the absorbed dose in gray (Gy). To convert to rad, recall that \( 1 \ \text{Gy} = 100 \ \text{rad} \).

Finally, calculate the dose equivalent \( H \) in mrem: \( H = D \cdot Q \cdot 1000 \), where the factor of 1000 converts rem to mrem. Use \( Q = 1 \) for beta radiation.

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주요 개념

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Radiation Dose

Radiation dose refers to the amount of energy deposited by ionizing radiation in a given mass of tissue. It is typically measured in grays (Gy) or rads, where 1 Gy equals 100 rads. In this context, the dose of 20 mJ (millijoules) of beta radiation needs to be converted into a dose unit that reflects the energy absorbed by the laboratory worker's body.

Dose Equivalent

Dose equivalent is a measure that accounts for the biological effect of different types of radiation on human tissue. It is expressed in sieverts (Sv) or rems, where 1 Sv equals 100 rems. The dose equivalent is calculated by multiplying the absorbed dose by a quality factor that reflects the type of radiation, allowing for a comparison of the potential biological impact of various radiation types.

Conversion to mrem

To express the dose equivalent in millirem (mrem), a common unit in radiation safety, one must convert the dose equivalent from rems. Since 1 rem equals 1000 mrem, the final calculation will involve converting the dose equivalent obtained from the absorbed dose and quality factor into mrem for practical understanding and safety assessments.