Ch.11 Nuclear Chemistry

McMurry - Fundamentals of General, Organic, and Biological Chemistry 8th Edition

McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187당신이 사용하는 게 아니라요?교과서 변경

McMurry 8th Edition

Ch.11 Nuclear Chemistry

문제 69

11장, 문제 69

If a radiation source has an intensity of 650 rem at 1.0 m, what distance is needed to decrease the intensity of exposure to below 25 rem, the level at which no effects are detectable?

검증된 단계별 안내

Understand that the intensity of radiation follows the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source. Mathematically, this is expressed as:

I_1/I_2 = (d_2/d_1)^2

, where

I_1

and

I_2

are the intensities at distances

d_1

and

d_2

, respectively.

Identify the given values:

I_1 = 650 \, \(\text{rem}\)

d_1 = 1.0 \, \(\text{m}\)

, and

I_2 = 25 \, \(\text{rem}\)

. The goal is to solve for

d_2

, the distance at which the intensity is reduced to below 25 rem.

Rearrange the inverse square law formula to solve for

d_2

d_2 = d_1 \(\sqrt{I_1/I_2}\)

Substitute the known values into the formula:

d_2 = 1.0 \, \(\text{m}\) \(\sqrt{650 \, \text{rem}\) / 25 \, \(\text{rem}\)}

. Simplify the ratio inside the square root.

Calculate the square root and multiply by

d_1

to find

d_2

. This will give the distance at which the intensity is reduced to below 25 rem.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Inverse Square Law

The Inverse Square Law states that the intensity of radiation decreases with the square of the distance from the source. This means that if you double the distance from the radiation source, the intensity of exposure is reduced to one-fourth. Understanding this principle is crucial for calculating how far one must be from a radiation source to achieve a desired intensity level.

Radiation Exposure Measurement

Radiation exposure is often measured in rems, which quantify the biological effect of ionizing radiation on human tissue. A level of 25 rem is considered the threshold below which no detectable effects occur. Familiarity with these units and their implications helps in assessing safety levels in radiation exposure scenarios.

Logarithmic Scale of Intensity

Radiation intensity often follows a logarithmic scale, meaning that small changes in distance can lead to significant changes in exposure levels. This concept is important when calculating the distance required to reduce exposure from a high level to a much lower one, as it emphasizes the non-linear relationship between distance and intensity.