Measures of Central Tendency: Mean, Median and Mode
1- Introduction2- Discovery of ruthenium and Occurrence.Fro
1. 1- Introduction
2- Discovery of ruthenium and Occurrence.
From( Properties and Applications of Ruthenium ) chapter of
boook
Link to citing information
https://www.intechopen.com/books/noble-and-precious-metals-
properties-nanoscale-effects-and-applications/properties-and-
applications-of-ruthenium
3-Chemical and physical properties
From( Properties and Applications of Ruthenium ) chapter of
boook
4-Compounds of Ru (refining of the platinum-Group Metals)
(Refining of the platinum-group metals)Chapter of book
Please make this part two pages.
5- Ruthenium complexes
From( Properties and Applications of Ruthenium ) chapter of
boook
6-Extraction (preparation of Ru)
1-CONCENTRATE COMPOSITION
3- SEPARATION TECHNIQUES USED IN THE REFINING OF
THE PLATINUM-GROUP METALS
From (Refining of the Platinum-Group
Metals) chapter of book.
7- General applications
From( Properties and Applications of Ruthenium ) chapter of
book.
2. 8-Catalytic activity of ruthenium, general application in
catalysis.
From( Properties and Applications of Ruthenium ) chapter of
book.
9- Application of Ru nanoparticles in catalysis
Articles (4– 9– 6 – 19-20) that6 articles you have done.
10- Application of Ru in some other different fields.
Articles (12-14-16-17-18- last article).
11- Summary and conclusions
From( Properties and Applications of Ruthenium ) chapter of
book.
12- References
Journal of
Materials Chemistry A
REVIEW
P
ub
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O
6. evolution
Sumei Han,†a Qinbai Yun,†b Siyang Tu,a Lijie Zhu,c Wenbin
Cao*a and Qipeng Lu *a
Developing a sustainable technology to produce hydrogen
efficiently is crucial to realize the “hydrogen
economy”, which may address the growing energy crisis and
environmental pollution nowadays.
Electrocatalytic and photocatalytic hydrogen evolution reactions
have received great attention during
the past few decades since they can realize hydrogen production
from the water splitting reaction
directly. Although platinum has been widely used as a catalyst
for the electrocatalytic and photocatalytic
hydrogen evolution reaction (HER), its high cost and limited
supply make it imperative to develop
alternative high-performance catalysts. Ruthenium (Ru), the
cheapest one among platinum-group
metals, has been emerging as a promising candidate recently.
Until now, tremendous efforts have been
devoted to improving the HER performance of metallic Ru-
based catalysts through the rational design
and synthesis of Ru nanomaterials, in which the size,
morphology, chemical composition and crystal
phase could be controlled. In this review, we summarized the
7. synthesis of various metallic Ru-based
nanomaterials as catalysts for the HER, including pure Ru
nanocrystals, Ru-based bimetallic
nanomaterials and Ru/non-metal nanocomposites. Then, we
covered the recent progress in the
utilization of metallic Ru-based nanomaterials as catalysts for
the electro- and photo-catalytic HER;
meanwhile, the mechanisms and fundamental science behind
morphology/composition/crystal
structure–performance relationships were discussed in detail.
Finally, the challenges and outlook are
provided for guiding the development of metallic Ru-based
electro- and photo-catalysts for further
fundamental research and practical applications in renewable
energy-related areas.
umei Han received her B.E.
egree from the University of
cience and Technology Beijing
n 2018. She is currently a Ph.D.
tudent under the supervision of
rof. Wenbin Cao and Prof.
ipeng Lu at the University of
cience and Technology Beijing.
er research interests are
elated to the development of
oble metal nanomaterials for
lectrocatalytic hydrogen
volution.
8. Wenbin Cao received his B.E.
degree from the Northeast Insti-
tute of Technology in 1992. He
obtained his M.E. degree from
Northeastern University in 1995
and completed his Ph.D. with
Prof. Changchun Ge at the
University of Science and Tech-
nology Beijing in 1998. He joined
the research group of Shourong
Yun at the Beijing Institute of
Technology as a postdoctoral
fellow. He worked in Osaka
University as a COE researcher from 2000 to 2002. Then he
joined
the University of Science and Technology Beijing. His current
research interests include photocatalysis, electromagnetic
absorbing
materials and phase transition materials.
g, University of Science and Technology
[email protected]; [email protected]
l of Materials Science and Engineering,
ng Avenue, Singapore 639798, Singapore
cSchool of Instrument Science and Opto-Electronics
Engineering, Beijing Information
Science and Technology University, Beijing 100192, China
† S. Han and Q. Yun contributed equally to this work.
hemistry 2019 J. Mater. Chem. A, 2019, 7, 24691–24714 |
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1. Introduction
The world-wide increasing energy demand makes it imperative
to the traditional and
rapidly depleting fossil fuels. Moreover, the consumption of
conventional fossil fuels has led to severe environmental
pollution and climate change.1,2 In order to solve the above
issues, since the 1970s, the concept of “hydrogen economy” has
been emerging to construct a clean and renewable energy
system based on the electrical energy generated by hydrogen.3,4
In this system, hydrogen gas (H2) serves as the energy carrier,
which can react with oxygen (O2) to generate electricity in fuel
cells, leaving water as the only byproduct (2H2 (g) + O2 (g) /
2H2O (l), DH ¼ �286 kJ mol�1).1,5,6 However, H2 does not
exist
abundantly in nature. Steam reforming of natural gas, partial
12. employed methods to produce H2 in industry. Although these
technologies could produce considerable amounts of H2 with
low cost, their utilization relies on fossil fuels with the
emission
of greenhouse gases, including carbon dioxide (CO2), nitrous
oxide and water vapor.7,8 Thus, it is of great importance to
develop a more sustainable technology to produce H2 and
realize the “hydrogen economy”.
The water splitting reaction is a well-known route to produce
H2 and O2 at the same time. The hydrogen evolution reaction
(HER), a half reaction of water splitting (2H+ + 2e� / H2), can
be driven by solar energy or electricity derived from other types
of renewable energy; thus there will be no CO2 emission during
the H2 production process.
9,10 Electrocatalytic hydrogen evolu-
tion will not generate any harmful by-products. Meanwhile, this
technology does not require large, centralized plants, which
could meet the requirements of different users from a large
scale (local fueling stations and industrial facilities) to a small
scale (individual households).11 But the high energy consump-
tion (180 MJ for 1 kg H2) and the short life time of
electrolyzers
are two main drawbacks of this technology.12 Improving the
electrocatalytic efficiency and prolonging the life time of
Qipeng Lu received his B.E.
degree from the Taiyuan Univer-
sity of Technology in 2008. He
obtained his M.E and Ph.D.
degrees from Beijing Jiaotong
University in 2010 and 2014,
respectively. As a visiting student,
he studied in Prof. Yadong Yin's
group at the University of Cal-
13. ifornia, Riverside, from 2011 to
2013. He then carried out his
postdoctoral research with Prof.
Hua Zhang at Nanyang Techno-
logical University, Singapore, in 2014. In 2018, he joined the
faculty
of the School of Materials Science and Engineering, University
of
Science and Technology Beijing. His research interests are
related to
the synthesis of nanostructured materials for energy conversion.
24692 | J. Mater. Chem. A, 2019, 7, 24691–24714
electrolyzers could reduce the cost of H2 production. One of the
most effective strategies is developing high-performance elec-
trocatalysts, which could reduce the overpotential during the
HER and thus lower electrical energy consumption.13
Currently,
the most utilized HER electrocatalyst is platinum (Pt) due to its
near-zero Gibbs free energy of adsorbed hydrogen (DGH),
which
means an appropriate hydrogen binding energy.14,15 For the
photocatalytic HER, Pt has also been the most frequently used
co-catalyst.16 The Pt co-catalyst can promote the separation of
electron–hole pairs and lower the activation barrier, thus facil-
itating photocatalytic reactions.17 However, the high cost and
limited world-wide supply of Pt severely hinders its large-scale
a lower
cost
is crucial for the development of clean H2 production by water
splitting.
Ruthenium (Ru), the cheapest one in platinum-group
metals, is a promising alternative HER catalyst since the bond
strength of Ru–H is comparable to that of Pt–H.18–20
14. Moreover,
Ru also exhibits good corrosion resistance in both acidic and
alkaline electrolytes.21 Although Ru colloids showed promising
catalytic activity for light-induced H2 evolution from water as
early as 1979,22 it is only recently that the utilization of Ru-
based
HER catalysts has received great attention with the advances of
nanotechnology. Preparation of metallic Ru-based nano-
materials is an effective strategy to increase the HER activity of
Ru, since more surface atoms serving as the active sites can be
exposed.23 The shape control of Ru-based nanomaterials is
effective in tuning the HER activity since different facets with
different atomic arrangements usually have diverse hydrogen
adsorption energies.24,25 Alloying Ru with other metals and
synthesizing bimetallic Ru-based core–shell nanomaterials
have also been proven as effective methods to enhance the HER
and
the synergetic effect between different metals.26,27 Moreover,
compositing Ru nanostructures with carbon, carbon nitride and
semiconductors could ensure that the active sites of Ru-based
nanomaterials are fully exposed, meanwhile preventing the
aggregation of the catalysts during the HER process.19,28–30
Normally, bulk Ru crystallizes in a hexagonal close packed
(hcp)
phase. Recently, it has been shown that Ru may crystalize in
face-centered cubic (fcc) or 4H phases under certain synthesis
conditions.28,31–34 As different arrangements of Ru atoms in
different crystal phases will change the electronic and
geometric structures of Ru-based catalysts,35 superior HER
activities are expected to be achieved in Ru nanomaterials with
unconventional crystal phases. From the aforementioned
aspects, the synthesis of metallic Ru-based nanomaterials and
their applications in the electrocatalytic and photocatalytic HER
are becoming a research hotspot; however, there has been no
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based nanomaterials for the electrocatalytic HER will be dis-
cussed. Next, we will introduce the use of metallic Ru-based
nanomaterials as co-catalysts for the photocatalytic HER.
Finally, we will give some perspectives on the challenges and
promising directions in this research area.
2. Synthesis of metallic Ru-based
nanomaterials
18. In the past few years, Ru-based electrocatalysts and photo-
catalysts have gained intensive research interests because of
their lower cost compared to Pt and high catalytic activity in the
HER.19,34 In order to effectively take advantage of Ru for the
HER, until now, various kinds of metallic Ru-based nano-
materials have been prepared, including pure Ru NCs, Ru-based
bimetallic nanomaterials and Ru/non-metal nanocomposites.
In the following sections, the synthesis methods of metallic Ru-
based nanomaterials will be introduced in detail.
2.1. Synthesis of pure Ru NCs
To achieve excellent catalytic activity, pure Ru NCs with
controllable size, morphology, exposed facet and crystal phase
have been synthesized through various wet chemical methods,
such as chemical reduction, hydro(solvo)thermal method and
template method. It is notable that bulk Ru normally adopts the
hcp crystal structure.35 With the development of crystal phase
engineering, Ru nanomaterials with fcc and 4H structures have
been synthesized because of the nanosize effect and exhibited
superior catalytic activity compared to hcp Ru nano-
materials.28,34,36 In this section, besides the morphology and
exposed facet control, we will focus on the synthetic procedures
of Ru NCs with these novel crystal phases.
Wang and co-workers synthesized Ru nanocluster colloids
via a chemical reduction method without using any protective
agents. The Ru nanoclusters with a size of around 1 to 2 nm are
very stable in solution, and no precipitation could be observed
and co-workers
synthesized fcc and hcp Ru nanoparticles (NPs) with tunable
size from 2.0 to 5.5 nm by simple chemical reduction methods,
respectively.36 They discovered that the crystal phase of Ru
NPs
varied with different metal precursors, and reducing and
stabilizing agents. When using RuCl3 as the metal precursor,
triethylene glycol (TEG) as the solvent and reducing agent, and
20. the crystal-phase based heterostructure, Huang and co-workers
synthesized Ru nanodendrites (Fig. 1b) composed of ultrathin
fcc/hcp nanoblades (Fig. 1c) via a facile solvothermal reduction
of Ru3+ together with Cu2+ followed by the selective etching
of
metallic Cu.21
Seed-mediated growth followed by chemical etching is an
effective synthetic approach to prepare Ru NCs with highly
open
structures such as NTs, NCGs and NFs. The synthetic process
mainly involves three steps: (i) preparing templates or seeds for
the deposition of Ru to form bimetallic nanostructures; (ii)
depositing Ru by epitaxial growth on the templates or metal
seeds; (iii) chemical etching to remove the templates.34 As
a typical example, Zhang's group reported that the hierarchical
4H/fcc Ru NTs could be synthesized by a hard template-medi-
ated method as shown in Fig. 1d, in which 4H/fcc Au nanowires
epitaxial growth of 4H/fcc Ru nanorods (NRs) (Fig. 1f).34 By
using Cu2+ in dimethylformamide as an effective etchant, the
Au templates were removed and hierarchical 4H/fcc Ru NTs
with ultrathin Ru shells and tiny Ru NRs were obtained (Fig.
1g).
Xia's group reported the successful synthesis of Ru cubic NCGs
with ultrathin walls, in which the Ru atoms were crystalized in
a fcc structure rather than the hcp structure.31 To obtain the Ru
cubic NCGs, Pd nanocubes (NCBs) served as seeds to realize
the
epitaxial growth of Ru and thereby formed the core–shell NCBs.
The Pd core was selectively etched away through the reaction
Pd
+ 2Fe3+ + 4Br� / PdBr4
2� + 2Fe2+ using an etchant based on the
Fe3+/Br� pair and then fcc cubic NCGs were obtained.
21. Moreover,
they also obtained octahedral41 and icosahedral39 Ru NCGs
with
ultrathin walls in the fcc phase by using a similar method. In
addition, fcc Ru NFs can also be obtained by realizing the
preferential growth of Ru on the corners and edges of Pd
truncated octahedra through kinetic control and then removing
the Pd seeds by chemical etching with the aid of the Fe3+/Br�
pair.32 Kinetic control was achieved by adjusting the injection
rate of the RuCl3$xH2O solution using a syringe pump while
the rates of the deposition and surface diffusion of Ru atoms
-
trodes without using any solvents, surfactants and reducing
agents. Cherevko and co-workers prepared a Ru/Ti/SiO2/Si
electrode for the HER and oxygen evolution reaction (OER) via
J. Mater. Chem. A, 2019, 7, 24691–24714 | 24693
Fig. 1 TEM images of (a) ultrathin Ru NSs. Reproduced with
permission.38 Copyright 2016, American Chemical Society. (b)
Ru nanodendrites.
Inset: the size distribution of Ru nanodendrites. (c) XRD
patterns of Ru and RuCu nanodendrites in comparison with the
standard peaks for hcp Ru
(JCPDS no. 06-0663), fcc Ru (JCPDS no. 88-2333) and fcc Cu
(JCPDS no. 04-0836). Reproduced with permission.21
Copyright 2018, The Royal
Society of Chemistry. (d) Schematic illustration of the
formation process of 4H/fcc Ru NTs. TEM images of (e) 4H/fcc
Au NWs, (f) 4H/fcc Au–Ru
NWs and (g) 4H/fcc Ru NTs. Reproduced with permission.34
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sputtering. During the preparation, single-crystal Si wafers with
a Ti adhesion layer, 300 nm of Ru was deposited on the
substrate at 250 W RF and 0.085 nm s�1.42
2.2. Synthesis of Ru-based bimetallic nanomaterials
According to the mixing pattern of Ru and the other metal, Ru-
based bimetallic nanomaterials can be divided into two types:
(i) Ru-based alloys and (ii) Ru-based core–shell structures. For
Ru-based alloys, two kinds of metals are distributed homoge-
neously in the NCs. However, for Ru-based core–shell struc-
tures, one kind of metal is located in the core and the other one
nucleates and grows surrounding the core to form a shell.
2.2.1. Synthesis of Ru-based alloys. Synthesizing Ru-based
alloys is an efficient strategy to combine the advantages of
different metals, generate a synergetic effect and reduce the
cost
of noble metal catalysts. The wet chemical approach has been
25. commonly used in the preparation of Ru-based bimetallic
alloys.
Li's group reported the synthesis of highly active and stable
Co-substituted Ru NSs for the HER through a solvothermal
method.43 They isolated Co atoms into Ru lattice by co-reduc-
tion of Ru(acac)3 and Co(acac)2 in a mixed solution containing
24694 | J. Mater. Chem. A, 2019, 7, 24691–24714
oleylamine and heptanol. Han and co-workers synthesized
a series of necklace-like hollow NixRuy nanoalloys based on
the
galvanic replacement reaction between Ni nanochains and
RuCl3$3H2O.
44 By adjusting the concentration of Ru precursors,
hollow NixRuy nanoalloys with variable Ni to Ru molar ratios
can be obtained due to the Kirkendall effect. Using Ru(acac)3
and Ni(acac)2 as metal precursors, Huang and co-workers re-
ported a wet chemical approach for the preparation of a three-
dimensional (3D) hierarchical structure composed of an ultra-
thin Ru shell and a Ru–Ni alloy core as a catalyst under
universal
pH conditions.45 By tuning the ratios of Ru/Ni precursors,
assemblies with different Ru/Ni ratios were obtained.
It should be noted that for Ru alloys with a non-hcp metal,
composition and the reduction kinetics of the different metal
precursors. Iversen and co-workers presented a systematic
investigation of the Pt1�xRux phase diagram through the
supercritic -
tional range, using an ethanol–toluene mixture as the solvent at
450 �C and 200 bar.46 The crystal phase, particle size and
morphology of the Pt1�xRux NPs were determined by the molar
ratio (i.e. x in Pt1�xRux). The crystallite and particle size of
the
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increased. The crystal phase of Pt1�xRux NPs was fcc when x #
0.2, while the hcp phase emerged as x approached 1. Besides,
the samples exhibited a spherical morphology as x < 0.3 while
elongated particles together with the dominating spherical
morphology were obtained when x $ 0.3. Although the crystal
phase of Ru-based alloys can be predicted using the phase
diagram, the nanosize effect makes it possible to obtain Ru-
based alloys with a novel structure beyond the phase diagram.
By using a chemical reduction method, Kitagawa's group suc-
ceeded in controlling the crystal structure of Au–Ru alloys with
a certain composition in the nanoscale.47 Normally, hcp Ru and
fcc Au do not easily form alloys in the bulk due to the large
lattice mismatch between these two elements. By precisely
tuning the reduction rate with the aid of cetyl-
trimethylammonium bromide (CTAB) and appropriate precur-
sors, fcc and hcp AuRu3 alloy NPs (Fig. 2a, b, c and d) can be
30. to the modulation of the geometric, strain and electronic
structures.
Solution
phase epitaxial growth is a versatile and facile
method to prepare Ru-based nanomaterials with core–shell
structures. As a prerequisite for heteroepitaxial growth, the
lattice mismatch between the seed and the secondary metal
should be small enough (<5%). When there is a large mismatch,
epitaxial growth is unfavorable due to high strain energy.27,49
In
this process, the deposited shell metal will follow the same
crystalline orientation as the core metal.26 Thus, it is possible
to
Ps. (c) XRD patterns of Au, fcc-AuRu3, hcp-AuRu3 and Ru
NPs. (d)The
s of AuRu3 alloy NPs with fcc and hcp crystal structures. RAu
and RRu are
ced with permission.47 Copyright 2018, Nature Publishing
Group.
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synthesize fcc Ru by epitaxial growth if a core metal with the
fcc
phase is selected. Li's group reported the synthesis of Pd–
[email protected] core–shell structures through an epitaxial-
growth-
mediated method, in which the crystal phase of the Ru shell can
be tuned from hcp to fcc.50 In the whole processes, a sol-
to prepare Pd–Cu alloy
seeds with a homogeneous truncated octahedral shape and
uniform size (19.6 �
was initially induced by galvanic replacement between Ru and
35. PdCu3 seeds. In this step, the structure of Pd–[email protected]
trans-
formed from core–shell into yolk–shell. Moreover, the experi-
mental results indicated that the PdCu3 and PdCu2.5 seeds were
PdCu2
or Cu seeds would drive the growth of the hcp Ru shell. As the
lattice parameter of Pd–Cu varied with the composition ratio of
Pd to Cu, the appropriate lattice mismatch between the Pd–Cu
alloy substrate and the Ru overlayer led to the epitaxial growth
of the Ru shell in the unconventional fcc phase. As another
example, by using Ru(acac)3 and Pd(acac)2 as metal precursors,
Yang and co-workers adopted a simple solvothermal method to
prepare [email protected] core–shell NPLs (Fig. 3a–c) with
various thick-
nesses and different crystal structures of the Ru shell by tuning
the amount of the Ru precursor.51 During the reaction, the fcc
Pd NPLs served as seeds for the epitaxial growth of the Ru shell
and the Ru atoms preferred to adopt a fcc structure rather than
a hcp structure owing to the similar atomic radii and the small
lattice mismatch between Pd and Ru. However, further increase
of Ru would result in a crystal phase transition of Ru from fcc
to
hcp since the regulation from Pd seeds for Ru growth became
weak with increasing thickness of the Ru shell.
36. Besides the fcc phase, Ru could also crystalize in some novel
crystal phases, e.g. the 4H phase, by epitaxial growth if unique
substrates are selected. For instance, using 4H/fcc Au NWs as
the initial seeds, Ru(acac)3 as the metal precursor,
Fig. 3 (a) TEM, (b) HAADF-HTEM image and (c) EDX
mapping of [email protected] N
of Chemistry. (d) Schematic illustration of the synthetic route
of Au–Ru N
enlarged sectional view illustrates the epitaxial growth of a Ru
NR on a Au
mapping of the Au–Ru NW. (g) HAADF-STEM images of Au–
Ru NWs. (g1
squares (areas g1 and g2) in (g). Reproduced with permission.33
Copyrigh
structures. Inset: the high magnification TEM image of the
[email protected] core
Royal Society of Chemistry.
24696 | J. Mater. Chem. A, 2019, 7, 24691–24714
octadecylamine as the solvent and surfactant, and 1,2-hex-
adecanediol as the reductant, 4H/fcc [email protected] NWs
with core–
shell structures could be prepared (Fig. 3d, e, f1 and f2).34
37. HAADF-STEM images and the corresponding statistical survey
showed that Ru NRs only deposited in the 4H phase and fcc-
twin boundary in the 4H/fcc Au NWs (Fig. 3g, g1 and g2),
indicating that the highly reactive 4H and fcc twin structures
could serve as preferential nucleation sites for the hetero-
epitaxial growth of the second metal. Meanwhile, the length of
Ru NRs could be easily tuned by varying the amount of the Ru
precursor. Moreover, in the synthesized bimetallic NWs, the Ru
NRs with highly active 4H or fcc-twin structures could serve as
nucleation sites for further growth of a third metal, such as Rh
or Pt, thus forming Au–Ru–Rh and Au–Ru–Pt hybrid NWs.34,52
Thermal reduction is also an effective approach for the
synthesis of Ru-based core–shell structures. A one-step
synthetic route was proposed by Joo's group to prepare hexag-
onal nanosandwich-shaped [email protected] core–shell
NPLs.53 The co-
decomposition of Ni and Ru precursors initially generated Ni
particles as cores with a hexagonal plate-
that, the Ru shell layer would deposit in a regioselective manner
on the top and bottom of the Ni NPLs as well as around its
center edges. The selective growth of the Ru shell layer can be
attributed to the distinct surface energies of different Ru facets
in the presence of CO gas, as well as the presence of twin
boundaries in the Ni core. This method can be extended to
38. synthesize trimetallic [email protected] core–shell NPs …
Photochemistry Assignment #4
This assignment covers material from Chapter 2 section 22 to
Chapter 2 Section 37.
1) Spin corresponds to the ________________________ angular
momentum of an
electron.
2) Electron spin, like electron exchange, is fundamentally a
quantum mechanical
phenomenon that has no classical analogue. However, like a
classical charged particle
spinning on an axis, an electron has a magnetic moment (µ).
Although a classical
spinning electron would possess a continuous range of angular
momentum values,
quantum mechanics demands that an individual electron has a
spin that has a fixed and
fundamental value of exactly __________ .
39. 3) Physical quantities that require both a magnitude and
direction in order to be fully
defined are called what?
4) Let the spin quantum number of some system be 3/2.
(a) What is the magnitude of the spin angular momentum
vector? In other words, what
is
S
r
?
(b) How many possible values of MS are there (the spin
multiplicity)?
(c) What are the values of MS?
(d) What are the values of the polar angle θ? In other words,
what are the possible
values of the angle that
S
40. r
makes with the z-axis?
5) What is the origin of the term “triplet state”?
6) According to the uncertainty principle of quantum
mechanics, if the value of SZ on the
z-axis is measured precisely, then the azimuthal angle’s position
in space will be
____________________________________________________
.
7) (a) The magnetic energy resulting from the interaction of a
magnetic moment µ and
an applied field HZ is known as what?
(b) The splitting of the energy into two or more levels when a
molecular system is
placed in an applied external magnetic field is known as the
effect.
41. 8) (a) The magnitude of the exchange interaction J is typically
much ____________
than that of magnetic interactions.
(b) What are the typical values of each?