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Absorbed dose refers to the amount of energy that radiation deposits in a unit mass of tissue. It describes how much energy from ionizing radiation is absorbed per kilogram of human tissue or other materials. This is important for understanding how radiation can affect the body on a cellular level.
The unit of absorbed dose is the gray (Gy), but in older literature, you might see the rad, where 1 Gy equals 100 rad. The formula used here to calculate absorbed dose in rads was \[\text{Absorbed Dose (D)} = \frac{\text{Total Energy Absorbed (in J)}}{\text{Mass (in kg)}} \times 100\]This shows the conversion factor thanks to which absorbed dose is often expressed in rads alongside modern units.

• For example, if a person absorbs 4.78 Joules of energy, and their body mass is 70 kg, you calculate the absorbed dose as 6.829 rad.

Understanding this concept helps us predict biological effects, making it a foundational notion in radiation dosimetry.

The equivalent dose takes the absorbed dose and modifies it with a factor that reflects the varying levels of biological impact of different types of radiation. This weighting factor acknowledges that some radiation types, like alpha particles, can be more damaging to biological tissues than others like X-rays or beta particles.
The equivalent dose uses the sievert (Sv) as its unit, but for historical notation, it can also be expressed in rems; where 1 Sv equals 100 rem.
To find the equivalent dose in rem, you multiply the absorbed dose by the radiation weighting factor for alpha particles, which is 20 according to the standard radiation protection guides:\[\text{Equivalent Dose (H)} = \text{Absorbed Dose} \times \text{Radiation Weighting Factor}\]
In our scenario, an absorbed dose of 6.829 rad is multiplied by 20 to get 136.58 rem, suggesting higher potential biological damage due to the nature of alpha particles' radiation.

• This concept helps us understand the potential impact on human health and aids in formulating safety standards.

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. A fundamental aspect of this process is half-life, the time taken for half of the radioactive nuclei in a sample to decay.
For radium-226 (^{226}Ra), which was used in our exercise, the half-life is 1600 years. This long half-life indicates that the radioactive substance remains active for a considerable time, continuing to emit radiation as it decays.

• The decay constant (\lambda), which helps calculate the decay rate, is determined by the formula: \[\lambda = \frac{0.693}{T_{1/2}}\]
• For ^{226}Ra, this was calculated as approximately 1.37 \times 10^{-11} \text{s}^{-1}.

This constant helps determine how many decays occur per second. It's crucial for calculating the activity of a radioactive source, which becomes evident in the next section.

The activity of a radioactive source is a measure of the number of decays occurring in a given time frame, expressed in becquerels (Bq), where 1 Bq equals 1 decay per second.
In the case of radium-226 with a mass given in the exercise:

• First, you need to determine the number of radioactive atoms (N), which is calculated using the formula \[N = \frac{\text{mass} \times N_A}{\text{molar mass}}\]
• Where N_A is Avogadro's number (6.022 \times 10^{23} ext{ mole}^{-1}), resulting in 8.53 \times 10^{19} atoms for the exercise.
• The activity (A)is then computed using \[A = \lambda \times N\]
• This produces an activity level of 1.17 \times 10^9 ext{ Bq} for the radium source.

Understanding activity is vital in assessing radiation safety, as it tells how radioactive materials might interact with the environment and human health over time.