Problem 59 - Chemistry The Molecular Science

Question

In 2012, a radiation reading of 73 sieverts (Sv) was recorded in the containment structure at the Fukushima Daiichi reactor 2 . Assuming a quality factor of 20 . convert this reading to: (a) rads. (b) grays (Gy). (c) mrem.

Step-by-Step Solution

Answer

73 Sv = 7300 rads, 73 Gy, and 7,300,000 mrem.

Step 1: Understanding the Problem

We need to convert a radiation dose of 73 sieverts to other units: rads, grays (Gy), and millirem (mrem). We are given a quality factor (QF) of 20.

Step 2: Converting Sieverts to Grays (Gy)

1 Sievert (Sv) is equivalent to 1 Gray (Gy) for the radiation dose. Therefore, a reading of 73 Sv is equal to 73 Gy because they are equivalent in terms of absorbed dose and biological effect considering QF is relevant for rem and Sv but not for Grays.

Step 3: Converting Sieverts to Rads

To convert sieverts to rads, we need to consider the relation between rads and grays. The conversion factor is 100 rads = 1 Gy. Since 73 Sv is equivalent to 73 Gy, we convert it to rads: \[73 ext{ Gy} imes 100 = 7300 ext{ rads}\]

Step 4: Converting Sieverts to mrem

To convert sieverts to millirem, we need to use the relation 1 Sv = 100 rem. Therefore, for millirem:\[73 ext{ Sv} imes 100 imes 1000 = 7,300,000 ext{ mrem}\]We multiply by 1000 to convert rem to mrem.

Key Concepts

Sieverts to Grays

Radiation is a complex subject, but understanding how to convert between different units can make it more approachable. When we talk about converting sieverts (Sv) to grays (Gy), we are dealing with measuring radiation dose. A sievert is a unit that refers to the biological effect of ionizing radiation, used primarily in the context of health physics, whereas a gray measures the absorbed dose of radiation. Fortunately, the conversion between these two units is straightforward. Both sieverts and grays represent the same amount of absorbed dose when the radiation quality factor (QF) is 1, as it is for gamma rays and x-rays. This means that 1 Sv equals 1 Gy. Therefore, if you have a radiation dose of 73 Sv, it is exactly the same as 73 Gy, assuming QF is relevant for Sv but not for Grays. This simplification applies because the definition of a sievert itself incorporates the QF, which makes the conversion directly proportional when discussing absorbed dose.

Sieverts to Rads

Now, let's see how to convert sieverts to rads. The rad is an older unit but still used in certain contexts, particularly in the United States. It measures the same quantity as grays, but on a different scale. While 1 Gy equals 100 rads, this gives us the pathway to convert sieverts into rads. Since we already established that 73 Sv equals 73 Gy, you can use this equivalence to convert to rads.

• First, convert grays into rads: 73 Gy × 100 = 7300 rads.

Thus, when you have a radiation dose in sieverts, converting to rads involves first thinking in terms of grays and then scaling up by a factor of 100. This allows us to smoothly transition between these radiation dose units.

Sieverts to mrem

Converting sieverts to millirem (mrem) is another important transformation, especially useful when dealing with smaller doses. The millirem is a subunit of the rem (roentgen equivalent in man), which like the sievert, also includes the biological risk of radiation into account. The conversion chain from sieverts to millirems is built on the relationship where 1 Sv equals 100 rem. Since 1 rem equals 1000 mrem, this leads to a simple conversion formula. To convert 73 Sv into mrem:

• First, calculate the rems: 73 Sv × 100 = 7300 rem.
• Then, convert rems to mrem: 7300 rem × 1000 = 7,300,000 mrem.

This approach helps to clarify how different scales of measurement affect the numbers we use but keep the actual amount of radiation consistent across units. Understanding these conversions allows you to compare readings from different measurement systems effectively.