It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans) using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of 12 mSv, applied to the whole body. By contrast, a chest x ray typically administers 0.20 mSv to only 5.0 kg of tissue. How many chest x rays would deliver the same total amount of energy to the body of a 75-kg person as one whole-body scan?

Verified step by step guidance

1. First, understand that the problem involves comparing the energy delivered by a whole-body CT scan to that delivered by multiple chest x-rays. The key is to equate the total energy imparted by both procedures.
2. The dose of radiation is given in millisieverts (mSv), which is a measure of the effect of radiation on the body. To find the energy, we need to convert this dose into energy using the formula: \( E = D \times m \), where \( E \) is the energy in joules, \( D \) is the dose in sieverts, and \( m \) is the mass of the tissue in kilograms.
3. Calculate the energy delivered by the whole-body scan: \( E_{\text{CT}} = 12 \text{ mSv} \times 75 \text{ kg} \). Convert mSv to Sv by dividing by 1000, since 1 Sv = 1000 mSv.
4. Calculate the energy delivered by one chest x-ray: \( E_{\text{chest}} = 0.20 \text{ mSv} \times 5.0 \text{ kg} \). Again, convert mSv to Sv by dividing by 1000.
5. To find the number of chest x-rays needed to deliver the same total energy as one whole-body scan, set \( n \times E_{\text{chest}} = E_{\text{CT}} \) and solve for \( n \), where \( n \) is the number of chest x-rays.

Key Concepts

Radiation Dose Measurement

Radiation dose is measured in sieverts (Sv), which quantifies the risk of exposure to ionizing radiation. It considers the type of radiation and its effect on different tissues. In this context, millisieverts (mSv) are used, where 1 Sv = 1000 mSv, to express the dose from medical imaging procedures like CT scans and x-rays.

Energy Absorption by Tissue

The energy absorbed by tissue from radiation is crucial for understanding the biological impact. It is calculated by multiplying the dose (in mSv) by the mass of the tissue exposed. For a whole-body scan, the dose is distributed over the entire body mass, while a chest x-ray targets a smaller mass, requiring conversion to compare total energy absorption.

Comparative Analysis of Radiation Procedures

To compare different radiation procedures, one must equate the total energy absorbed by the body. This involves calculating the energy from each procedure and determining how many of one type (e.g., chest x-rays) equate to another (e.g., whole-body CT scan) by considering the dose and mass of tissue exposed in each scenario.