ACHIEVE/CHEMICAL PRINCIPLES ACCESS 2TERM
ACHIEVE/CHEMICAL PRINCIPLES ACCESS 2TERM
7th Edition
ISBN: 9781319403959
Author: ATKINS
Publisher: MAC HIGHER
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Chapter 1, Problem 1B.28E

(a)

Interpretation Introduction

Interpretation:

The minimum uncertainty in the speed of an electron confined in a nanoparticle with a diameter of 2.00×102nm has to be calculated.

Concept Introduction:

Uncertainty principle:

Uncertainty principle states that if the location of a particle is known to within an uncertainty Δx, then the linear momentum, p, parallel to the x – axis can be known simultaneously only to within an uncertainty Δp.

Mathematically, Δp×Δx12

Where, Δx is the uncertainty in position and Δp is the uncertainty in momentum.

(a)

Expert Solution
Check Mark

Answer to Problem 1B.28E

The minimum uncertainty in the speed of an electron confined within a lead atom of diameter 350pm is 1.65×105m/s.

Explanation of Solution

Given that, the uncertainty in position of an electron is 2.00×102nm.  The mass of electron is 9.109×1031kg.

The uncertainty principle says that,

  Δp×Δx=12mΔv×Δx=12Δv=2mΔx

By plugging all data in the above equation, the value of uncertainty in the speed of electron can be calculated.

  Δv=2mΔx=1.05457×1034J.s2×(9.109×1031kg)×(2.00×107m)Δv=289.43×J.skg.mΔv=289.43×kg.m2.s2.skg.m=289.43m/sΔv=289.43m/s

Therefore, the minimum uncertainty in the speed of an electron confined within a nanoparticle of diameter 2.00×102nm is 289.43m/s.

(b)

Interpretation Introduction

Interpretation:

The minimum uncertainty in the speed of a Li+ confined in a nanoparticle with a diameter of 2.00×102nm has to be calculated.

Concept Introduction:

Refer to part (a).

(b)

Expert Solution
Check Mark

Answer to Problem 1B.28E

The minimum uncertainty in the speed of a confined within a Li+ nanoparticle of diameter 2.00×102nm is 2.25×10-5m/s.

Explanation of Solution

Given that, the uncertainty in position of a Li+ is 2.00×102nm.  The mass of a Li+ ion can be calculated as given below.

Li+ has two electrons, three protons and four neutrons.

  massofLi+=2×massofelectron+3×massofproton+4××massofneutronmassofLi+=2×0.000548579909u+3×1.00727647u+4×1.00866491588umassofLi+=7.06u1molLi+=6.023×1023ionsmassof1Li+ion=7.06u×(1molLi+6.023×1023Li+ions)massof1Li+ion=1.17×10-23kg

The uncertainty principle says that,

  Δp×Δx=12mΔv×Δx=12Δv=2mΔx

By plugging all data in the above equation, the value of uncertainty in the speed of a Li+ can be calculated.

  Δv=2mΔx=1.05457×1034J.s2×(1.17×10-23kg)×(2.00×107m)Δv=2.25×105J.skg.mΔv=2.25×105×kg.m2.s2.skg.m=2.25×105m/sΔv=2.25×10-5m/s

Therefore, the minimum uncertainty in the speed of a confined within a Li+ nanoparticle of diameter 2.00×102nm is 2.25×10-5m/s.

(c)

Interpretation Introduction

Interpretation:

The one which could be specified more accurately in a nanoparticle: the speed of an electron or the speed of a Li+ ion has to be determined.

Concept Introduction:

Refer to part (a).

(c)

Expert Solution
Check Mark

Explanation of Solution

The uncertainty in speed of an electron and a Li+ ion confined in a nanoparticle with a diameter of same size are 289.43m/s and 2.25×10-5m/s respectively.

The uncertainty in speed of a Li+ ion is very small in comparison to an electron confined in a nanoparticle of same size.  Therefore, the speed of an electron could be specified more accurately in a nanoparticle.

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Chapter 1 Solutions

ACHIEVE/CHEMICAL PRINCIPLES ACCESS 2TERM

Ch. 1 - Prob. 1A.8ECh. 1 - Prob. 1A.9ECh. 1 - Prob. 1A.10ECh. 1 - Prob. 1A.11ECh. 1 - Prob. 1A.12ECh. 1 - Prob. 1A.13ECh. 1 - Prob. 1A.14ECh. 1 - Prob. 1A.15ECh. 1 - Prob. 1A.16ECh. 1 - Prob. 1A.17ECh. 1 - Prob. 1B.1ASTCh. 1 - Prob. 1B.1BSTCh. 1 - Prob. 1B.2ASTCh. 1 - Prob. 1B.2BSTCh. 1 - Prob. 1B.3ASTCh. 1 - Prob. 1B.3BSTCh. 1 - Prob. 1B.4ASTCh. 1 - Prob. 1B.4BSTCh. 1 - Prob. 1B.5ASTCh. 1 - Prob. 1B.5BSTCh. 1 - Prob. 1B.1ECh. 1 - Prob. 1B.2ECh. 1 - Prob. 1B.3ECh. 1 - Prob. 1B.4ECh. 1 - Prob. 1B.5ECh. 1 - Prob. 1B.6ECh. 1 - Prob. 1B.7ECh. 1 - Prob. 1B.8ECh. 1 - Prob. 1B.9ECh. 1 - Prob. 1B.10ECh. 1 - Prob. 1B.11ECh. 1 - Prob. 1B.12ECh. 1 - Prob. 1B.13ECh. 1 - Prob. 1B.14ECh. 1 - Prob. 1B.15ECh. 1 - Prob. 1B.16ECh. 1 - Prob. 1B.17ECh. 1 - Prob. 1B.18ECh. 1 - Prob. 1B.19ECh. 1 - Prob. 1B.21ECh. 1 - Prob. 1B.22ECh. 1 - Prob. 1B.23ECh. 1 - Prob. 1B.24ECh. 1 - Prob. 1B.25ECh. 1 - Prob. 1B.26ECh. 1 - Prob. 1B.27ECh. 1 - Prob. 1B.28ECh. 1 - Prob. 1C.1ASTCh. 1 - Prob. 1C.1BSTCh. 1 - Prob. 1C.1ECh. 1 - Prob. 1C.2ECh. 1 - Prob. 1C.3ECh. 1 - Prob. 1C.7ECh. 1 - Prob. 1D.1ASTCh. 1 - Prob. 1D.1BSTCh. 1 - Prob. 1D.2ASTCh. 1 - Prob. 1D.2BSTCh. 1 - Prob. 1D.1ECh. 1 - Prob. 1D.2ECh. 1 - Prob. 1D.3ECh. 1 - Prob. 1D.4ECh. 1 - Prob. 1D.5ECh. 1 - Prob. 1D.6ECh. 1 - Prob. 1D.7ECh. 1 - Prob. 1D.9ECh. 1 - Prob. 1D.10ECh. 1 - Prob. 1D.11ECh. 1 - Prob. 1D.12ECh. 1 - Prob. 1D.13ECh. 1 - Prob. 1D.14ECh. 1 - Prob. 1D.15ECh. 1 - Prob. 1D.16ECh. 1 - Prob. 1D.17ECh. 1 - Prob. 1D.18ECh. 1 - Prob. 1D.19ECh. 1 - Prob. 1D.20ECh. 1 - Prob. 1D.21ECh. 1 - Prob. 1D.22ECh. 1 - Prob. 1D.23ECh. 1 - Prob. 1D.24ECh. 1 - Prob. 1D.25ECh. 1 - Prob. 1D.26ECh. 1 - Prob. 1E.1ASTCh. 1 - Prob. 1E.1BSTCh. 1 - Prob. 1E.2ASTCh. 1 - Prob. 1E.2BSTCh. 1 - Prob. 1E.1ECh. 1 - Prob. 1E.2ECh. 1 - Prob. 1E.3ECh. 1 - Prob. 1E.4ECh. 1 - Prob. 1E.5ECh. 1 - Prob. 1E.7ECh. 1 - Prob. 1E.8ECh. 1 - Prob. 1E.9ECh. 1 - Prob. 1E.10ECh. 1 - Prob. 1E.11ECh. 1 - Prob. 1E.12ECh. 1 - Prob. 1E.13ECh. 1 - Prob. 1E.14ECh. 1 - Prob. 1E.15ECh. 1 - Prob. 1E.16ECh. 1 - Prob. 1E.17ECh. 1 - Prob. 1E.18ECh. 1 - Prob. 1E.19ECh. 1 - Prob. 1E.20ECh. 1 - Prob. 1E.21ECh. 1 - Prob. 1E.22ECh. 1 - Prob. 1E.23ECh. 1 - Prob. 1E.24ECh. 1 - Prob. 1E.25ECh. 1 - Prob. 1E.26ECh. 1 - Prob. 1F.1ASTCh. 1 - Prob. 1F.1BSTCh. 1 - Prob. 1F.2ASTCh. 1 - Prob. 1F.2BSTCh. 1 - Prob. 1F.3BSTCh. 1 - Prob. 1F.1ECh. 1 - Prob. 1F.2ECh. 1 - Prob. 1F.3ECh. 1 - Prob. 1F.4ECh. 1 - Prob. 1F.5ECh. 1 - Prob. 1F.6ECh. 1 - Prob. 1F.7ECh. 1 - Prob. 1F.8ECh. 1 - Prob. 1F.10ECh. 1 - Prob. 1F.11ECh. 1 - Prob. 1F.12ECh. 1 - Prob. 1F.13ECh. 1 - Prob. 1F.14ECh. 1 - Prob. 1F.15ECh. 1 - Prob. 1F.17ECh. 1 - Prob. 1F.18ECh. 1 - Prob. 1F.19ECh. 1 - Prob. 1F.22ECh. 1 - Prob. 1.1ECh. 1 - Prob. 1.2ECh. 1 - Prob. 1.3ECh. 1 - Prob. 1.9ECh. 1 - Prob. 1.10ECh. 1 - Prob. 1.11ECh. 1 - Prob. 1.12ECh. 1 - Prob. 1.13ECh. 1 - Prob. 1.14ECh. 1 - Prob. 1.15ECh. 1 - Prob. 1.17ECh. 1 - Prob. 1.19ECh. 1 - Prob. 1.21ECh. 1 - Prob. 1.22ECh. 1 - Prob. 1.23ECh. 1 - Prob. 1.24ECh. 1 - Prob. 1.25ECh. 1 - Prob. 1.27ECh. 1 - Prob. 1.28ECh. 1 - Prob. 1.31E
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