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 68b

11장, 문제 68b

A selenium-75 source is producing 300 rem at a distance of 2.0 m?
b. What is its intensity at 25 m?

검증된 단계별 안내

Step 1: Understand the problem. The intensity of radiation follows the inverse square law, which states that the intensity of radiation 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.

Step 2: Identify the given values. From the problem, we know:

I_1 = 300 \, \(\text{rem}\)

d_1 = 2.0 \, \(\text{m}\)

, and

d_2 = 25 \, \(\text{m}\)

. We need to calculate

I_2

, the intensity at 25 m.

Step 3: Rearrange the inverse square law formula to solve for

I_2

. The formula becomes:

I_2 = I_1 \(\cdot\) \(\left\)(\(\frac{d_1}{d_2}\)\(\right\))^2

Step 4: Substitute the known values into the formula. Replace

I_1

with 300 rem,

d_1

with 2.0 m, and

d_2

with 25 m. The equation becomes:

I_2 = 300 \(\cdot\) \(\left\)(\(\frac{2.0}{25}\)\(\right\))^2

Step 5: Simplify the expression to calculate

I_2

. First, calculate the fraction

\(\frac{2.0}{25}\)

, then square the result, and finally multiply by 300 to find the intensity at 25 m.

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주요 개념

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Radiation Intensity

Radiation intensity refers to the power per unit area carried by a wave, typically measured in watts per square meter (W/m²). In the context of radiation sources, intensity decreases with distance from the source due to the inverse square law, which states that intensity is inversely proportional to the square of the distance from the source.

Inverse Square Law

The inverse square law is a fundamental principle in physics that describes how a physical quantity (like light or radiation) decreases as the distance from the source increases. Specifically, if the distance from the source doubles, the intensity becomes one-fourth of its original value. This law is crucial for calculating changes in intensity at different distances.

Radiation Measurement Units

Radiation is often measured in units such as rem (roentgen equivalent man), which quantifies the biological effect of ionizing radiation on human tissue. Understanding these units is essential for interpreting radiation exposure and its potential health impacts, as well as for converting between different measurement systems when calculating intensity.

A selenium-75 source is producing 300 rem at a distance of 2.0 m? b. What is its intensity at 25 m?