Ch.11 Nuclear Chemistry

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

McMurry8th EditionFundamentals of General, Organic, and Biological ChemistryISBN: 9780134015187Not the one you use?Change textbook

McMurry 8th Edition

Ch.11 Nuclear Chemistry

Problem 69

Chapter 11, Problem 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?

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

A selenium-75 source is producing 300 rem at a distance of 2.0 m?

b. What is its intensity at 25 m?

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Textbook Question

Harmful chemical spills can often be cleaned up by treatment with another chemical. For example, a spill of H₂SO₄ might be neutralized by addition of NaHCO₃. Why is it that the harmful radioactive wastes from nuclear power plants cannot be cleaned up as easily?

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Textbook Question

Why is a scintillation counter or Geiger counter more useful for determining the existence and source of a new radiation leak than a film badge?

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Textbook Question

Why are rems the preferred units for measuring the health effects of radiation?

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Textbook Question

Film badge dosimeters typically include filters to target specific types of radiation. A film badge is constructed that includes a region containing a tin foil filter, a region containing a plastic film filter, and a region with no filter. Which region monitors exposure to α-radiation? Which monitors exposure to β-radiation? Which monitors γ-radiation? Explain.

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Textbook Question

What does it mean when we say that strontium-90, a waste product of nuclear power plants, has a half-life of 28.8 years?