BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Solutions

Chapter
Section
BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

You might wonder how it is possible to determine the half-life of long-lived radioactive isotopes such as 238U. With a half-life of more than 109 years, the radioactivity of a sample of uranium will not measurably change in your lifetime. In fact, you can calculate the half-life using the mathematics governing first-order reactions.

It can be shown that a 1.0-mg sample of 238U decays at the rate of 12 α emissions per second. Set up a mathematical equation for the rate of decay, ΔNt = −kN, where N is the number of nuclei in the 1.0-mg sample and ΔNt is 12 dps. Solve this equation for the rate constant for this process, and then relate the rate constant to the half-life of the reaction. Carry out this calculation, and compare your result with the literature value, 4.5 × 109 years.

Interpretation Introduction

Interpretation: To calculate the rate constant for the radioactive isotope of uranium-238 by using first order reaction and compared with the literature value.

Concept introduction:

The rate of decay can be calculated by the following formula:

  ΔNΔt= -kN

Here,

  K is the rate constant

  N is the number of nuclei in 1.0mg of sample (Avogadro number=6.02×1023).

Explanation

Given information as follows:

ΔN/Δt = 12dps

The number of nuclei is 1.0mg.

The literature value of rate constant is 4.5×109years

The rate of decay can be calculated by the following formula:

ΔN/Δt=kN

Here,

K=Rate constant

N=Number of nuclei in 1.0mg of sample (Avogadro number=6.02×1023).

N=1.0mg238000mg/mol× 6.02 × 1023atom/mol= 4.201×10-6×6.02×1023= 25

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Additional Science Solutions

Find more solutions based on key concepts

Show solutions add

What is am absolute temperature scale? How are degrees Celsius related to kelvins?

General Chemistry - Standalone book (MindTap Course List)

Which of these B vitamins is (are) present only in foods of animal origin? a. niacin b. vitamin c. riboflavin d...

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

How many autosomes are present in a body cell of a human being? In a gamete?

Human Heredity: Principles and Issues (MindTap Course List)

What is the defining feature of a synovial joint?

Human Biology (MindTap Course List)