A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. If the RBE of the radiation is 9.5, calculate the effective absorbed dose in mrem and Sv.

Verified step by step guidance

Understand the given values: The activity of the radiation source is 14.3 mCi (millicuries), and the Relative Biological Effectiveness (RBE) is 9.5.

Convert the activity from millicuries to becquerels (Bq) using the conversion factor: 1 Ci = 3.7 × 10^10 Bq. Therefore, 1 mCi = 3.7 × 10^7 Bq.

Calculate the absorbed dose in rad. The absorbed dose in rad can be calculated using the formula: \( \text{Absorbed dose (rad)} = \frac{\text{Activity (Bq)}}{\text{Mass (kg)}} \times \text{Energy per decay (J)} \). Note: You may need additional information such as the energy per decay and the mass of the rat to proceed with this calculation.

Calculate the dose equivalent in rem using the formula: \( \text{Dose equivalent (rem)} = \text{Absorbed dose (rad)} \times \text{RBE} \).

Convert the dose equivalent from rem to sieverts (Sv) using the conversion factor: 1 rem = 0.01 Sv. Therefore, \( \text{Dose equivalent (Sv)} = \text{Dose equivalent (rem)} \times 0.01 \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radioactivity and Activity Units

Radioactivity refers to the process by which unstable atomic nuclei lose energy by emitting radiation. The activity of a radioactive source is measured in curies (Ci) or millicuries (mCi), where 1 Ci equals 3.7 x 10^10 disintegrations per second. Understanding the activity of a source is crucial for calculating the potential exposure and effects on biological tissues.

Relative Biological Effectiveness (RBE)

Relative Biological Effectiveness (RBE) is a factor used to compare the biological effectiveness of different types of radiation. It accounts for the varying damage caused by different radiation types, with higher RBE values indicating greater potential for biological harm. In this case, an RBE of 9.5 means that the alpha radiation is 9.5 times more effective at causing biological damage than a reference radiation, typically gamma rays.

Absorbed Dose and Dose Conversion

The absorbed dose is the amount of energy deposited by radiation in a given mass of tissue, measured in grays (Gy) or rads. To express this in terms of biological effect, it is often converted to sieverts (Sv) using the RBE. The effective absorbed dose can be calculated by multiplying the absorbed dose by the RBE, allowing for a comparison of the potential health risks associated with different types of radiation exposure.

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A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (a) What is the activity of the radiation in disintegrations per second? In becquerels?

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Textbook Question

A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (b) The rat has a mass of 385 g and is exposed to the radiation for 14.0 s, absorbing 35% of the emitted alpha particles, each having an energy of 9.12 * 10-13 J. Calculate the absorbed dose in millirads and grays.

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