   # A certain radioactive nuclide has a half-life of 3.00 hours. a. Calculate the rate constant in s −1 for this nuclide. b. Calculate the decay rate in decays/s for 1.000 mole of this nuclide. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 74CWP
Textbook Problem
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## A certain radioactive nuclide has a half-life of 3.00 hours.a. Calculate the rate constant in s−1 for this nuclide.b. Calculate the decay rate in decays/s for 1.000 mole of this nuclide.

(a)

Interpretation Introduction

Interpretation: Half life of a certain radioactive nuclide is given. The rate constant in s-1 for this nuclide is to be calculated. The decay rate in decays/s for 1 mole of this nuclide is to be calculated.

Concept introduction: Unstable nuclides become stable by emitting radiation such as alpha, beta, and gamma particles and this is known as radioactive decay. Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second. Half life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

To determine: The rate constant in s-1 for the given nuclide.

### Explanation of Solution

Explanation

The rate constant can be calculated by the formula given below.

λ=0.693t1/2

Where,

t1/2 is the half life.

λ is the rate constant.

The value of t1/2 is 3hours .

The conversion of hours into minutes is done as,

1hour=60minutes

Therefore, the conversion of 3hours into minutes is,

3hours=3×60minutes=180minutes

The conversion of minutes into seconds is done as,

1minute=60seconds

Therefore, the conversion of 180 <

(b)

Interpretation Introduction

Interpretation: Half life of a certain radioactive nuclide is given. The rate constant in s-1 for this nuclide is to be calculated. The decay rate in decays/s for 1 mole of this nuclide is to be calculated.

Concept introduction: Unstable nuclides become stable by emitting radiation such as alpha, beta, and gamma particles and this is known as radioactive decay. Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second. Half life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

To determine: The decay rate in decays/s for 1 mole of the given nuclide.

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