Question

If a woman is exposed to \(57 \mathrm{mrem} / \mathrm{yr}\) of radiation because of medical X-rays and her total exposure is \(360 \mathrm{mrem} / \mathrm{yr}\), what percentage of her total exposure is due to medical X-rays?

Short answer

Approximately 15.83% of her total exposure is due to medical X-rays.

Step-by-step solution

Identify the total exposure and exposure due to X-rays

The total exposure is given as 360 mrem/yr, and the exposure due to medical X-rays is 57 mrem/yr.

Calculate the percentage of total exposure due to X-rays

Use the formula for percentage: \( \frac{\text{part}}{\text{whole}} \times 100 \). Here, 'part' is the exposure due to X-rays (57 mrem/yr) and 'whole' is the total exposure (360 mrem/yr). So the calculation is \( \frac{57}{360} \times 100 \).

Perform the Calculation

Divide 57 by 360 and then multiply by 100 to find the percentage: \( \frac{57}{360} \times 100 \approx 15.83 \% \).

Key concepts

Percentages in Chemistry

Understanding percentages in chemistry is key to grasping the relative amounts of substances in mixtures, solutions, or even the distribution of elements in various compounds. In the context of radiation exposure, percentages are used to represent how much of the total radiation exposure comes from a specific source.

For example, when we calculate the percentage of radiation exposure due to medical X-rays, we're essentially dividing the 'part' (the radiation from X-rays) by the 'whole' (the total radiation exposure) and then multiplying by 100 to express the result as a percentage. It's crucial to ensure that units cancel out properly and that both quantities being compared are measured in the same units.

This concept is similar to determining the concentration of a solution in chemistry, where one might calculate the percentage of a solute in a solution to understand its strength or to adjust it for various uses. It's a straightforward application of ratios and fractions, bridging real-world examples like radiation exposure with fundamental chemical principles.

Radiation Measurement

Radiation measurement involves quantifying the amount of energy that comes from ionizing radiation sources, such as X-rays or radioactive materials. The unit used in the exercise, 'mrem' or millirem, is a unit of radiation dosage commonly used in the United States. One millirem (1 mrem) is one thousandth of a rem, which stands for Roentgen equivalent man, a measure of the health effect of low levels of ionizing radiation on the human body.

In radiation measurement, it is crucial to understand not just how much radiation is being measured but also the potential impact on health. Different types of radiation have different biological impacts, and thus they are measured using equivalent doses to ensure that all radiation types are weighted according to their potential effects. For example, the dose equivalent in sieverts (Sv), which is widely used outside of the United States, takes into account the type of radiation and its biological effects.

When working with problems involving radiation measurement, one must be versed in the proper conversion between units if necessary, and understand the different types of radiation measurements and their context within health physics and safety regulations.

Medical X-rays Impact

Medical X-rays are a critical diagnostic tool, but they also contribute to an individual's overall exposure to ionizing radiation. While they offer incredible benefits in diagnosing and treating medical conditions, it is crucial to understand their impact on health due to the ionizing nature of X-rays.

Ionizing radiation can remove tightly bound electrons from atoms, potentially leading to cellular damage, which contributes to the risk of cancer. However, medical X-rays are carefully regulated to minimize this risk by using the lowest exposure necessary for the required medical imaging. The impact of X-rays is assessed in terms of dose received and the risk it poses to the patient.

In the context of our exercise, by establishing that a certain percentage of the total radiation dose comes from medical X-rays, healthcare providers can analyze and optimize patient care, ensuring that the benefits of imaging procedures clearly outweigh the risks associated with radiation exposure. It is the balance of these risks and benefits that underlines the continuous evaluation and advancement in medical imaging technology, emphasizing safer techniques and lower doses.