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 12

Chapter 11, Problem 12

A β-emitting radiation source gives 250 units of radiation at a distance of 4.0 m. At what distance does the radiation drop to one-tenth its original value?

Verified step by step guidance

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 can be expressed as \( I \propto \frac{1}{d^2} \), where \( I \) is the intensity and \( d \) is the distance.

Set up the relationship: Let the initial intensity \( I_1 \) be 250 units at a distance \( d_1 = 4.0 \, \text{m} \). The final intensity \( I_2 \) is one-tenth of the original intensity, so \( I_2 = \(\frac{I_1}{10}\) = 25 \, \(\text{units}\).

Use the inverse square law formula: \( \frac{I_1}{I_2} = \left( \frac{d_2}{d_1} \right)^2 \). Substitute \( I_1 = 250 \), \( I_2 = 25 \), and \( d_1 = 4.0 \, \text{m} \) into the equation.

Solve for \( d_2 \): Rearrange the formula to isolate \( d_2 \): \( d_2 = d_1 \sqrt{\frac{I_1}{I_2}} \). Substitute the known values into the equation.

Perform the calculation: Calculate \( d_2 \) using the values substituted in the previous step to determine the distance at which the radiation drops to one-tenth its original value.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

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 from a point source decreases with the square of the distance from the source. This means that if you double the distance from the source, the intensity of radiation is reduced to one-fourth. This principle is crucial for understanding how radiation levels change with distance.

Radioactive Decay

Radioactive decay refers to the process by which unstable atomic nuclei lose energy by emitting radiation. The rate of decay is characterized by the half-life, which is the time required for half of the radioactive atoms in a sample to decay. Understanding this concept helps in determining how radiation levels decrease over distance and time.

Radiation Dose Measurement

Radiation dose measurement quantifies the amount of radiation energy absorbed by an object or person. It is often expressed in units such as grays (Gy) or sieverts (Sv). Knowing how to measure and interpret radiation doses is essential for assessing exposure levels and understanding the implications of radiation on health and safety.

Recommended video:

Guided course

02:52

Measuring Radioactivity Concept 1

Related Practice

Textbook Question

A 1.00 mL sample of red blood cells containing chromium-51 as a tracer was injected into a patient. After several hours, a 5.00 mL sample of blood was drawn and its activity compared to the activity of the injected tracer sample. If the collected sample activity was 0.10% of the original tracer, calculate the total blood volume of the patient (see the Chemistry in Action 'Medical Uses of Radioactivity,' p. 338).

views

Textbook Question

A solution of selenium-75, a radioisotope used in the diagnosis of pancreatic disease, is found just prior to administration to have an activity of 44 μCi/mL. If 3.98 mL were delivered intravenously to the patient, what dose of Se-75 (in μCi) did the patient receive?

views

Textbook Question

A typical chest X ray exposes a patient to an effective dose of 0.02 mSv. How many rem is this, and how many chest X rays would a patient have to receive before biological effects would be observed? (The limit from Table 11.6 is >25 rem.)

views

Textbook Question

Identify and write the symbol for each of the five nuclides in the decay series shown in Problem 11.25.

views

Textbook Question

The red arrow in the graph (see margin) indicates the changes that occur in the nucleus of an atom during a nuclear reaction. Identify the isotopes involved as product and reactant, and name the type of decay process.

views