ATKINS' PHYSICAL CHEMISTRY-ACCESS
ATKINS' PHYSICAL CHEMISTRY-ACCESS
11th Edition
ISBN: 9780198834700
Author: ATKINS
Publisher: OXF
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Chapter 15, Problem 15B.3P
Interpretation Introduction

Interpretation:

The unit cell of silver, the unit cell dimension and mass density of silver has to be determined.

Concept Introduction:

Bragg’s law:

  nλ=2dhklsinθ

Where,

λ= Wavelength of incident light

dhkl= Interplanar distance

2θ= Glancing angle

n= Order of diffraction

  Density =Z×mV×NA

Where,

Z= Formula unit

V= volume of one unit cell

NA= Avogadro’s no.

m= Mass of a substance per mole

Expert Solution & Answer
Check Mark

Answer to Problem 15B.3P

The unit cell of silver, the unit cell dimension and mass density of silver has been found out to be FCC, 408.5518pm and 10.5081g/cm3 respectively.

Explanation of Solution

Given data:

  θ=19.076,22.171,32.256λ=154.18pm

Expected reflections:

  BravislatticeReflectionspresentforReflectionsabsentforPrimitivesimplecubicAllEx.(100),(110),(111)etc.NoneBCCh+k+l=evenEx.(110),(200),(211)etc.h+k+l=oddFCCh,kandl=unmixed(allevenorodd)Ex.(111),(200)(220)etc.h,kandl=mixed

According to Bragg’s relationship,

  nλ=2dhklsinθdhkl=nλ2sinθ=154.18pm2×sin(19.076)=235.8775pm[bytakingn=1]dhkl=nλ2sinθ=154.18pm2×sin(22.171)=204.2811pmdhkl=nλ2sinθ=154.18pm2×sin(32.256)=144.4436pm

This calculation is according to given data in the question.

Expected dhkl for simple cubic:

  nλ=2dhklsinθd100=a12+02+02=a=235.8775pmd110=a12+12+02=a2=166.7905pmd111=a12+12+12=a3=136.1839pm

But it is not matching with the calculated value.

Expected dhkl for BCC:

  nλ=2dhklsinθd110=a12+12+02=a2=235.8775pmd200=a22+02+02=a2=2a2=2×235.8775pm2=166.7891pmd211=a22+12+12=a6=2a6=136.1839pm

But it is not matching with the calculated value.

Expected dhkl for FCC:

  nλ=2dhklsinθd111=a12+12+12=a3=235.8775pmd200=a22+02+02=a2=3a2=3×235.8775pm2=204.2759pmd220=a22+22+12=a3=3a3=136.1839pm

It is matching with the calculated value.

Hence, the cubic unit cell of silver is FCC and the cell dimension is (3×235.8775pm)408.5518pm.

Now, molar mass of silver is 107.9g/mol and Z=4.

  Density=4×107.9g/mol(408.5518×1010)3×6.023×1023=10.5081g/cm3.

Therefore, the mass density of silver is found out to be 10.5081g/cm3.

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Chapter 15 Solutions

ATKINS' PHYSICAL CHEMISTRY-ACCESS

Ch. 15 - Prob. 15A.2AECh. 15 - Prob. 15A.2BECh. 15 - Prob. 15A.3AECh. 15 - Prob. 15A.3BECh. 15 - Prob. 15A.4AECh. 15 - Prob. 15A.4BECh. 15 - Prob. 15A.1PCh. 15 - Prob. 15A.2PCh. 15 - Prob. 15A.3PCh. 15 - Prob. 15A.4PCh. 15 - Prob. 15A.5PCh. 15 - Prob. 15A.6PCh. 15 - Prob. 15A.7PCh. 15 - Prob. 15A.8PCh. 15 - Prob. 15A.9PCh. 15 - Prob. 15B.1DQCh. 15 - Prob. 15B.2DQCh. 15 - Prob. 15B.3DQCh. 15 - Prob. 15B.1AECh. 15 - Prob. 15B.1BECh. 15 - Prob. 15B.2AECh. 15 - Prob. 15B.2BECh. 15 - Prob. 15B.3AECh. 15 - Prob. 15B.3BECh. 15 - Prob. 15B.4AECh. 15 - Prob. 15B.4BECh. 15 - Prob. 15B.5AECh. 15 - Prob. 15B.5BECh. 15 - Prob. 15B.6AECh. 15 - Prob. 15B.6BECh. 15 - Prob. 15B.7AECh. 15 - Prob. 15B.7BECh. 15 - Prob. 15B.11AECh. 15 - Prob. 15B.11BECh. 15 - Prob. 15B.12AECh. 15 - Prob. 15B.12BECh. 15 - Prob. 15B.1PCh. 15 - Prob. 15B.2PCh. 15 - Prob. 15B.3PCh. 15 - Prob. 15B.4PCh. 15 - Prob. 15B.6PCh. 15 - Prob. 15B.7PCh. 15 - Prob. 15C.1DQCh. 15 - Prob. 15C.2DQCh. 15 - Prob. 15C.1AECh. 15 - Prob. 15C.2AECh. 15 - Prob. 15C.2BECh. 15 - Prob. 15C.3AECh. 15 - Prob. 15C.3BECh. 15 - Prob. 15C.4AECh. 15 - Prob. 15C.4BECh. 15 - Prob. 15C.5AECh. 15 - Prob. 15C.5BECh. 15 - Prob. 15C.1PCh. 15 - Prob. 15C.2PCh. 15 - Prob. 15C.3PCh. 15 - Prob. 15C.4PCh. 15 - Prob. 15C.5PCh. 15 - Prob. 15C.7PCh. 15 - Prob. 15C.8PCh. 15 - Prob. 15C.9PCh. 15 - Prob. 15D.1DQCh. 15 - Prob. 15D.1AECh. 15 - Prob. 15D.1BECh. 15 - Prob. 15D.2AECh. 15 - Prob. 15D.2BECh. 15 - Prob. 15D.3AECh. 15 - Prob. 15D.3BECh. 15 - Prob. 15D.1PCh. 15 - Prob. 15D.2PCh. 15 - Prob. 15E.1DQCh. 15 - Prob. 15E.1AECh. 15 - Prob. 15E.1BECh. 15 - Prob. 15E.2AECh. 15 - Prob. 15E.2BECh. 15 - Prob. 15E.3AECh. 15 - Prob. 15E.3BECh. 15 - Prob. 15E.5PCh. 15 - Prob. 15F.1DQCh. 15 - Prob. 15F.1AECh. 15 - Prob. 15F.1BECh. 15 - Prob. 15F.2AECh. 15 - Prob. 15F.2BECh. 15 - Prob. 15F.3AECh. 15 - Prob. 15F.3BECh. 15 - Prob. 15F.4AECh. 15 - Prob. 15F.4BECh. 15 - Prob. 15F.5AECh. 15 - Prob. 15F.5BECh. 15 - Prob. 15G.1DQCh. 15 - Prob. 15G.2DQCh. 15 - Prob. 15G.1AECh. 15 - Prob. 15G.1BECh. 15 - Prob. 15.1IA
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