Principles of Instrumental Analysis
7th Edition
ISBN: 9781305577213
Author: Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher: Cengage Learning
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Chapter 12, Problem 12.3QAP
Interpretation Introduction
Interpretation:
Approximate wavelength of V, Ni, Se, Br, Cd and Sb for ka lines is to be calculated.
Concept introduction:
Approximate wavelength of elements is calculated by preparing spreadsheet of elements then plotting the graph
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The energy levels of hydrogenlike one-electron ions of atomic number Z differ from those of hydrogen by a factor of Z2. Predict the wavelength of the 2s ->1s transition in He+.
Sulphur presents two lines: Ka₁= 5.37216 Å and Ka₂= 5.37496 Å
1. What is the energy difference expressed in eV, between Ka₁ and Kα₂
2. If it is known that the width at the mid-height of these lines is 5 eV, what conclusion can be
drawn
3. If the position of the Ka₂ line increases by 0.002 Å when passing from S6+ to Sº, show that
this has no impact upon the location of this photoelectron in energy terms
Part B
The electronic structure of one-dimensional chain of sodium (Na) atoms can be approximately described by the particle-in-a-box model. The energy of each state can be calculated using En=(n^2h^2)/8mL^2, ? = 1, 2, 3, … where L is the length of the 1D chain. Assuming L = a0(N – 1), where N is the number of Na atoms and a0 = 0.360 nm is the internuclear distance.
a) Determine the energy gap between the highest occupied energy level and the lowest unoccupied energy level as a function of N. Assume that N is an even number that is large enough (Hint: assume that each Na only contributes 1 electron to the problem and consider the information in Question 1c above.).
b) Thermal energy at room temperature is 4.15 × 10–21 J. Calculate the minimum number of Na atoms required so that the energy gap is smaller than the thermal energy.
Chapter 12 Solutions
Principles of Instrumental Analysis
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