Question

(a) If a chest x ray delivers 0.25 mSv to 5.0 kg of tissue, how many $total$ joules of energy does this tissue receive? (b) Natural radiation and cosmic rays deliver about 0.10 mSv per year at sea level. Assuming an RBE of 1, how many rem and rads is this dose, and how many joules of energy does a 75-kg person receive in a year? (c) How many chest x rays like the one in part (a) would it take to deliver the same $total$ amount of energy to a 75-kg person as she receives from natural radiation in a year at sea level, as described in part (b)?

Short answer

(a) 0.00125 J; (b) 0.01 rem, 0.01 rads, 0.0075 J; (c) 6 chest X-rays.

Step-by-step solution

Convert mSv to Sv for Part (a)

The dose in millisieverts (mSv) needs to be converted to sieverts (Sv) to find the total energy. Since 1 Sv equals 1000 mSv, we convert 0.25 mSv to Sv. This gives us:$$0.25\text{ mSv}=0.25\times {10}^{-3}\text{ Sv}$$

Calculate Energy in Joules for Part (a)

To find the energy in joules, we use the relation $1\text{ Gy (Gray)}=1\text{ J/kg}$, and 1 Sv is equivalent to 1 Gy when the RBE (Relative Biological Effectiveness) is 1. Multiply the dose in Sv by the mass in kg and by 1J/kg:$$\text{Energy}=0.25\times {10}^{-3}\text{ Sv}\times 5\text{ kg}=1.25\times {10}^{-3}\text{ J}$$

Convert mSv to rem for Part (b)

Since 1 Sv = 100 rem, convert 0.10 mSv to rem. Thus:$$0.10\text{ mSv}=0.10\times {10}^{-3}\times 100=0.01\text{ rem}$$

Convert mSv to rads for Part (b)

Similarly to rem, we convert mSv to rads assuming RBE = 1. Hence, 1 mSv = 0.1 rads. Therefore:$$0.10\text{ mSv}=0.01\text{ rads}$$

Calculate Energy in Joules for Part (b)

The energy absorbed by the 75-kg person is calculated in the same way: multiply the dose in Sv by the mass. First convert 0.10 mSv to Sv:$$0.10\text{ mSv}=0.10\times {10}^{-3}\text{ Sv}$$Now calculate energy:$$\text{Energy}=0.10\times {10}^{-3}\text{ Sv}\times 75\text{ kg}=7.5\times {10}^{-3}\text{ J}$$

Calculate Number of X-rays Needed for Part (c)

For this step, divide the total energy from natural radiation in a year (7.5 x 10^-3 J) by the energy from one X-ray (1.25 x 10^-3 J):$$\text{Number of X-rays}=\frac{7.5\times {10}^{-3}\text{ J}}{1.25\times {10}^{-3}\text{ J}}=6$$

Key concepts

Energy Absorption

Energy absorption in the context of radiation dosimetry refers to the process by which energy from ionizing radiation is deposited in a medium, usually biological tissue. This is a fundamental concept, as the energy absorbed is what leads to potential biological effects. The energy is measured in joules, and depending on the problem, it's calculated using the mass of the absorbing tissue and the dose the tissue receives in terms of absorbed dose units like Grays (Gy).

In the exercise provided, the energy absorbed by the tissue is found using the formula:

• The dose in sieverts (Sv) multiplied by the mass of the tissue.
• Keep in mind, the unit Gray (Gy) is used for the absorbed dose, and 1 Gy equals 1 joule/kilogram (J/kg).

This method translates the dose into an amount of energy deposited in the tissue. By using specific conversions, we determine that a small x-ray dose resulted in the absorption of a fraction of a joule in a 5 kg tissue.

Radiation Units Conversion

Radiation units conversion plays a critical role in understanding and comparing radiation doses received from different sources. Several units are used in radiation dosimetry, including Sieverts (Sv), rems, and rads, each representing different aspects of radiation dose. Converting between these units is crucial for expressing doses in the most appropriate or familiar way for a given context.

Here are some key conversion factors:

• 1 Sievert (Sv) is equivalent to 100 rem. This conversion is often used when dealing with biological effects since Sv measures the biological impact of the absorbed dose.
• 1 milliSievert (mSv) is 1000 times smaller than 1 Sv, hence converting mSv to Sv requires multiplying by 0.001.
• Rads are used primarily in the United States, with 1 Gray (Gy) equal to 100 rads. Rads denote the absorbed dose of radiation.

By performing conversions correctly, like in the exercise where millisieverts were converted to rem and rads, one can accurately interpret and compare radiation exposure in different scenarios, such as seeing how natural radiation stacks up against x-ray exposure.

Relative Biological Effectiveness (RBE)

Relative Biological Effectiveness (RBE) is a measure used in radiobiology to compare the biological effectiveness of different types of ionizing radiation. Different radiations given the same absorbed dose can have varying effects on biological tissues; RBE is a factor that quantifies these differences.

Key considerations for RBE include:

• RBE takes into account the type of radiation and the biological context, like the type of tissue or the biological endpoint (e.g., cell death or genetic mutation).


• An RBE value of 1 indicates that the radiation type has a standard level of biological effectiveness, which is what typical x-rays are assigned.


• Higher RBE values would mean the radiation is more damaging per unit dose than x-rays or gamma rays.

In the given exercise, the RBE was assumed to be 1, which shows that the type of radiation involved, standard x-rays and cosmic radiation, have a baseline effect as determined against a comparable radiation type. Factoring RBE provides a deeper understanding of potential risks associated with different radiation forms, crucial for accurate dosimetry and safety assessments.