# Which of the following statement(s) is(are) true ? a. A radioactive nuclide that decays from 1.00 × 10 10 atoms to 2.5 × 10 9 atoms in 10 minutes has a half-life of 5.0 minutes. b. Nuclides with large Z values are observed to be α -particle producers. c. As Z increases, nuclides need a greater proton-to-neutron ratio for stability. d. Those “light” nuclides that have twice as many neutrons as protons are expected to be stable.

### Chemistry: An Atoms First Approach

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

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 78CWP
Textbook Problem
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## Which of the following statement(s) is(are) true?a. A radioactive nuclide that decays from 1.00 × 1010 atoms to 2.5 × 109 atoms in 10 minutes has a half-life of 5.0 minutes.b. Nuclides with large Z values are observed to be α-particle producers.c. As Z increases, nuclides need a greater proton-to-neutron ratio for stability.d. Those “light” nuclides that have twice as many neutrons as protons are expected to be stable.

(a)

Interpretation Introduction

Interpretation: The authentication of the given statements is to be checked.

Concept introduction: Nuclei of radioactive element decompose in various ways.  There are two major categories. One involves a change in mass number of the decaying nucleus while others do not.  Types of radioactive processes include α particle production, β particle production, γ ray production, electron capture and many others.

### Explanation of Solution

Explanation

The given statement is true.

The decay constant (λ) is calculated by the formula,

ln(NN0)=λt

Where,

• N is the atoms of nuclide after decay.
• N0 is the number of atoms of radioactive nuclide originally.
• t is the decay time.

The value of N is 2.5×109 atoms.

The value of N0 is 1×1010 atoms.

The decay time is 10 minutes .

Substitute the value of N , N0 and decay time in the above equation.

ln(NN0)=λtln2.5×1091×1010=λ×10 minutes1

(b)

Interpretation Introduction

Interpretation: The authentication of the given statements is to be checked.

Concept introduction: Nuclei of radioactive element decompose in various ways.  There are two major categories. One involves a change in mass number of the decaying nucleus while others do not.  Types of radioactive processes include α particle production, β particle production, γ ray production, electron capture and many others.

(c)

Interpretation Introduction

Interpretation: The authentication of the given statements is to be checked.

Concept introduction: Nuclei of radioactive element decompose in various ways.  There are two major categories. One involves a change in mass number of the decaying nucleus while others do not.  Types of radioactive processes include α particle production, β particle production, γ ray production, electron capture and many others.

(d)

Interpretation Introduction

Interpretation: The authentication of the given statements is to be checked.

Concept introduction: Nuclei of radioactive element decompose in various ways.  There are two major categories. One involves a change in mass number of the decaying nucleus while others do not.  Types of radioactive processes include α particle production, β particle production, γ ray production, electron capture and many others.

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