C 06J
General Chemistry
Course Outline (7 lectures)
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The Structure of the Atom
Atomic particles: protons, neutron and electrons
Mass Relationships of Atoms
Atomic number, mass number, isotopes, mass and atomic spectroscopy
(line spectra- Rydberg equation and the Balmer series)
The Electronic Structure of the Atom
Bohr model
The wave nature of the electron
Quantum numbers, atomic orbitals, electronic configuration
The periodic table
Atomic Structure
 Matter
 Anything that has mass and occupies space
 It exists in three states: solid, liquid and gas
 Element
 A substance that cannot be chemically broken down
further
 For example, hydrogen, sodium, chlorine, silicon
Atomic Structure
 The Greek philosopher proposed that matter
is made up tiny particles called atoms
 Atom: derived from the Greek word Atomos
(indivisible)
Dalton’s Atomic Theory
John Dalton (1766-1844)
 Elements are made up of tiny particles called atoms
 Atoms of the same element have the same mass (definite
average mass), while atoms of different elements have
different masses
 Atoms of the same element are chemically alike and atoms
different elements are chemically different. Elements
combine chemically in whole number ratios to form
different substances
 Atoms are not changed during chemical reactions
 This theory does not explain what the atom is made up of
Structure of the Atom
 Evidence supporting the structure of the atom was
gathered using radioactive elements
 Several scientists conducted experiments that led to
what is known today as the structure of the atom
 The atom consists of a positively charged nucleus
 The nucleus is very small and dense and has a
diameter of 10-12 cm
 1 Angstrom (Å) = 10-8 cm
 Therefore diameter of the nucleus is 10-4 Å
 Diameter of the atom is 1-5 Å
Structure of the atom
Evidence supporting the
presence of a nucleus
 Experiment conducted by English physicist Ernest Rutherford
 In an evacuate tube, a beam of alpha particles were directed at a thin
gold sheet
 Most of the particles passed through the sheet
 A few were slightly deflected
 Very few were greatly deflected (1 in 20,000)
 It was assumed that the alpha particles bounced back if they approached
a positively charged nucleus head on
 Those that were slighly deflected passed close to the nucleus
 Most particles passed straight through the gold foil, which implied that
the atom consists of a lot of space
Rutherford’s Experiment
www.sol.sci.uop.edu/~jfalward/physics17/chapter13/chapter113.html
The Nucleus
 Except for the hydrogen atom, the nucleus of every atom
consists of two types of particles: protons and neutrons
 Protons
 Positively charged
 Mass: 1.673 x 10-24 g
 The positive charge is equal in magnitude to the negative
charge on the electron
 In each atom # of protons = # of electrons
 As a result the atom is neutral
The Nucleus
 Neutrons
 Discovered by English scientist James C. Chadwick in 1932
 Neutral particles (no electric charge)
 Mass: 1.6375 x 10-24 g
Thomson’s Experiment
 This experiment involved the use of a cathode ray tube
 This is a glass tube from which the air has been removed and with two pieces of
metals called electrodes attached
 An electric current flows through the tube when a sufficient voltage is applied
 The current flow is from the cathode (negatively charged) to the anode
(positively charged)
 If the tube is not fully evacuated and still contains small amounts of air or other
gases, the current flow is visible as a glow called a cathode ray
 This beam is produced at the negative electrode and is deflected towards the
positive electrode
 The beam can also be deflected by a magnet or an electrically charged plate
 Thomson proposed that the cathode ray must consist of tiny negatively charged
particle called electrons
 Being emitted from different kinds of metal, elements must contain electrons
Thomson’s Cathode Ray Tube Experiment
http://online.cctt.org.physicslab/content/phy2HON/lessonnotes/modern/electronbeams.asp
Electrons
 Discovered by English scientist J. J.
Thompson
 These are negatively charged particles
 They move about the nucleus with different
energies
 Mass: 9.110 x 10-28 g
 Radius: 2.818 x 10-13 cm
Structure of the Atom
Comparison of Subatomic
Particles
Particle
Mass/g
Mass/amu Charge/C Charge/e
Electron
9.109 x 10-28
5.486 x 10-4
-1.602 x 10-19
-1
Proton
1.673 x 10-24
1.007
+1.602 x 10-19
+1
Neutron
1.675 x 10-24
1.009
0
0
Atomic and Mass Number
 Atomic Number (Z)
 The number of protons present in the nucleus
 The number of electrons around the nucleus
 Mass number (A)
 The sum of the number of protons (Z) and neutrons
(N) present in the nucleus
 A=Z+N
Isotopes
 The number of protons is not always equal to the number of
neutrons
 Therefore atoms of the same element can have different
mass numbers
 These are called isotopes
 For example, Hydrogen has three isotopes
 Isotopes behave almost identical in their chemical reactions,
the number of neutrons present has very little effect on the
atoms chemical property
 The chemical property is determined by the number of
electrons present
Isotopes of Hydrogen
Protium
1 proton
0 neutron
1 electron
http:/encarta.msn.com/media_461531710_-1_1/Hydrogen_Isotopes.html
Exercise
 How many protons, neutrons and electrons
are present in this isotope of uranium 23592U?
Answer
 92 protons
 92 electrons
 143 neutrons
Atomic Weight
 An element’s atomic weight is a weighted average of the
isotopic masses of the element’s naturally occurring
isotopes
 The mass of an atom is extremely small in grams and so is
measured in atomic mass units (amu) instead
 1 amu = 1/12 mass of carbon-12 = 1.66054 x 10-24 g
 For example, carbon
Exercise
 Copper metal has two naturally occurring
isotopes copper-63 (69.17%, isotopic mass
62.94 amu) and copper-65 (30.83%, isotopic
mass 64.93 amu). Calculate the atomic
weight of copper.
Electromagnetic Spectrum
 Made up of a range of electromagnetic
radiation
 Electromagnetic radiation is characterised by
frequency, wavelength and amplitude
www.cem.msu.edu/~reusch/virtualtext/spectrpy/UV-Vis/spectrum.htm
Visible Light/White Light
www.cem.msu.edu/~reusch/virtualtext/spectrpy/UV-Vis/spectrum.htm
www.cem.msu.edu/~reusch/virtualtext/spectrpy/UV-Vis/spectrum.htm
Wave Characteristics
 Frequency (ν): number of wave peaks or
cycles per unit time. Units: s-1 or Hertz
 Wavelength (λ): distance from one crest or
wave peak to another. Units: nm
 Amplitude: the height of the wave from the
center line between peaks and troughs
Wave Characteristics
www.cem.msu.edu/~reusch/virtualtext/spectrpy/UV-Vis/spectrum.htm
Waves
 The rate at which electromagnetic radiation travels
is referred to as the speed of light c
 Speed of light = 2.997 x 108 m/s
 Wavelength (m) x Frequency (s-1) = Speed (m/s)
 c=λxν
 λ and ν are inversely related
 The light blue glow given off by mercury lamps has
a wavelength of 436 nm. What is its frequency?
Exercise
 What is the wavelength (in meters) of an FM
radio wave with frequency ν = 102.5 MHz
and a medical X ray with ν = 9.55 x 1017 Hz?
Last Lecture
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Structure of the atom
Subatomic particles
Rutherford’s experiment
Thomson’s experiment
Atomic number
Mass number, atomic mass unit
Isotopes
Electromagnetic spectrum
Waves characteristics (c = λ ν)……..λ and ν are inversely related
Atomic Spectra
 Visible light consists of a continuous distribution of wavelengths, i.e.400
(violet)-700 (red) nm
 These different wavelengths travel at different rates through a prism
resulting in the splitting of of white light into the various different
colours
 When atoms are excited they give off visible light
 This visible light given off by an excited atom is not in the form of a
continuous distribution as with light from the sun
 Instead it consists of only a few wavelengths
 This results in a series of lines and blank spaces called a line spectrum
Line Spectra
http://neon.chem.uidaho.edu/~honours/spectra
http://csep10.phys.utk.edu/astra162/lect/light/absorption.html
Atomic Spectra
 Each element has its own line spectrum
 Na: yellow light
 K: purple light
 For hydrogen, a spectrum of four lines is produced at 656.3
nm (red), 481.6 nm (blue-green), 434.0 nm (blue) and 410.1
nm (indigo).
 According to Johann Balmer these wavelengths could be
expressed as:
 1/λ = R {1/22 – 1/n2} (Balmer Equation)
 R = Rydberg constant (1.097 x 10-2 nm-1)
 n = integer greater then 2
Atomic Spectra
 Line spectra are also present in the non-visible region of the
spectrum
 These give rise to spectral line called Lyman series (far UV)
as well as Paschen, Brackett and Pfund series (IR region)
 Those resulting from the visible region are referred to as the
Balmer series
 Jahannes Rydberg used the Balmer equation to show that
every aspect of the spectrum can fit the equation
 This resulted in the Balmer-Rydberg equation
Balmer-Rydberg Equation
 1/λ = R {1/m2-1/n2}
 Lyman series, m = 1
 Balmer series, m = 2
 Paschen series, m = 3
 m and n are integers, where n is greater than
m
Points to note
 Light can behave like waves as well as small
particles (so far we have looked at the wave characteristics)
 Excited electrons do not give off/emit light of
continuous wavelength
 As a result, this does not give a continuous
spectrum
 Light of specific energy is emitted (quantum)
giving rise to a line spectrum
Questions
 What are the two longest wavelengths lines
(in nm) in the Lyman series of the hydrogen
spectrum?
 What is the shortest wavelength line (in nm)
in the Lyman series of the hydrogen
spectrum?
Exercise
 The Balmer equation can be extended
beyond the visible portion of the
electromagnetic spectrum to include lines in
the ultraviolet. What is the wavelength (in
nanometers) of ultraviolet light in the Balmer
series corresponding to a value of n = 7?
Particle-like Properties of
Electromagnetic Radiation
 Blackbody radiation: visible glow given off by
objects when heated
 The intensity of black body radiation varies with
the wavelength of the light emitted
 As an object is heated, the colour change is dull red
 bright orange  white
 The intensity does not rise indefinitely
 Instead, it reaches a maximum (λ = 500 nm) and
then falls rapidlyIntensity of Blackbody Radiation
vs. Wavelength
Explanation
 The intensity of black body radiation does not rise
indefinitely
 Therefore the energy given off cannot be
continuous
 It is quantised, i.e. emitted in discrete units
called quanta
 The energy of this radiation depends on the
frequency
Planck Equation
 E = hν
 h = Planck’s constant (6.626 x 10-34 Js)
 We already know that ν = c/λ
 Therefore E = hc/λ
Question
 Calculate the energy of one quantum of red
light of frequency 4.62 x 1014 s-1 and
wavelength 649 nm.
Recall
 Shorter wavelengths imply high frequency
 Longer wavelengths imply low frequency
 The energy of radiation/light depends on the
frequency NOT intensity.
Exercise
 What is the energy of photons of FM
radiowaves with ν = 102.5 MHz
Particle-like Properties of
Electromagnetic Radiation
 For an electron to be ejected from the surface of a
metal the light or energy supplied must be above a
certain threshold value
 This threshold is different for every metal
 Einstein assumed that a beam of light behaves like a
stream of particles with specific amounts of
energies/frequencies
 These particles are called photons
 If the frequency is not above the threshold value,
then no electron is ejected
Wave-like Properties of Matter
 de Broglie suggested that if light can behave like
matter (having particle characteristics), then matter can also
exhibit some properties similar to those of light (i.e.
wave-like properties)
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Both have wave and particle characteristics
Energy, E = mc2
(Einstein)
m = E/c2
m = mass of photon, c = speed of light
According to Planck, E = hc/λ
hc/ λ = mc2
de Broglie Equation
 de Broglie suggested that this equation could be
applied to an electron by replacing the speed of
light (photon) c with that of the speed of the
electron, v
 As a result, the wavelength of an electron can be
calculated
 Hence:
 de Broglie equation λ = h/mv
Question
 What is the de Broglie wavelength of an
electron of mass 9.11 x 10-31 kg and velocity
2.2 x 106 ms-1?
Exercise
 What is the de Broglie wavelength of a
pitched baseball with a mass of 120 g and a
speed of 100 mph (44.7 m/s)?
Exercise
 What is the de Broglie wavelength (in
meters) of a small car with mass 1150 kg
travelling at a speed of 55.0 mph (24.6 m/s)?
The Electronic Structure of the
Atom
 Bohr Model
 Bohr described the atom as a nucleus with an electron
orbiting it, similar to the planets orbiting the sun
 Certain orbits correspond to specific energy levels that are
available to the electron
 Electrons have specific energy levels available to them
 Model failed for atoms with more than one electron
 The path is now considered to be less definite
 Rather than a strict path, the electron seems to occupy
empty space around the nucleus (electron cloud)
Quantum Mechanical Model
 This abandons the notion of an electron as a
small particle that moves in a specific path
around the nucleus
 It focuses on the wavelike properties of the
electron
 Werner Heisenburg showed that it is
impossible to know exactly where the
electron is and what path it follows
Wave Function/Orbital
 Has a specific energy associated with it
 It contains information about the electron’s position (3D)
 For H atom the lowest energy level available to an electron
is associated with the wave function called a 1s orbital
 An electron in a 1s orbital will occupy a spherical region of
space around the nucleus
 The electron is most likely to be found closer to the nucleus,
and less likely to be found as you move further away from
the nucleus
 The electron’s path or movement is uncertain
 It assumes a wavelike description, rather than a particle like
description
Wave Function and Quantum
Numbers
 A wave function or orbital describes the behaviour
of an electron (position & path)
 Each wave function contains three variables called
quantum numbers
 These are represented as n, l and ml
 They describe the energy level of the orbital as well
as the shape and orientation of the region of space
in which an electron will be found
The Principal Quantum Number
(n)
 This is a positive integer (n = 1,2,3…)
 It determines the size and energy level of the orbital
 As n increases the number of allowed orbitals
increase and the size of the orbitals become larger
 This allows for electrons to be located far from the
nucleus
 As n increases the energy of the electron in the
orbital also increases
 According to n, orbitals are grouped into layers
called shells around the nucleus
The Principal Quantum Number
(n)
n=1
n=2
n=3
n=4
K shell
L shell
M shell
N shell
The Angular-momentum/Orbital
Quantum Number (l)
 This defines the three dimensional shape of the
orbital in which the electron moves
 The number of possible shapes is equal to the
principal quantum number
 When the principal quantum number is n, the
angular-momentum quantum number has values
from 0 to n-1
 According to l, orbitals are grouped into subshells
referred to as s, p, d, f
The Magnetic Quantum
Number (ml)
 This defines the spatial orientation of the orbital
along a standard set of coordinate axes
 When the angular-momentum quantum number is l,
the magnetic quantum number has values from –l to
+l
 For a group of orbitals having the same principal
quantum number n, and the same shape l, the
different spatial orientations for the orbital is (2l+1)
The Spin Quantum Number ms
 This indicates the property of the electron described
by two conditions
 It can be thought of as being right-handed or lefthanded, clockwise or counter clockwise
 Electron spin
 It can have either of two values: +1/2 or –1/2
 The spin quantum number is independent of the
first three quantum numbers
Quantum Numbers
 The position of the orbital described by the
first three quantum numbers can be occupied
by two electrons, but these must have
opposite spins
 No two electrons can have the same set of
four quantum numbers (Pauli Exclusion
Principle)
 No two electrons can have the same energy
Question
 Identify the shell and subshell of an electron
with the quantum numbers: n = 3, l = 1 and
ml = 1
Exercise
 Give the possible combinations of quantum
numbers for a 4p orbital.
Exercise
 Give the possible combinations of quantum
numbers for the following orbitals:
 (a) 3s
 (b) 2p
 (c) 4d
Exercise
 Give the orbital notations for electrons with
the following quantum numbers:
 (a) n = 2, l = 1, ml = 1
 (b) n = 4, l = 3, ml = -2
 (c) n = 3, l = 2, ml = -1
Explanation of Line Spectrum using the
quantum mechanical model
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Electrons occupy orbitals
Orbitals have specific energy levels
The energy available to electrons are quantized
When an atom is heated, the energy causes an electron to jump from one
energy level to another (i.e. from a lower energy orbital to a higher
energy orbital)
The excited atom is unstable and quickly returns to the lower energy
level
This is accompanied by emission of the amount of energy that was
added (i.e. the difference between the higher and lower energy orbitals)
The energy of the orbitals are quantized, and the energy emitted is also
quantized
As a result, we observe the emission of only specific frequenices of
radiation
 The variables m and n in the Balmer –
Rydberg equation for hydrogen corresponds
to the principal quantum numbers of the two
orbitals involved in the electronic transition
Question
 What is the energy difference (kJ/mol)
between the first and second shells of the
hydrogen atom if the first emission in the
Lyman series occurs at λ = 121.5 nm?
Orbital Shapes
 This corresponds to the angular-momentum
quantum number (ℓ)
 The designations are s, p, d, f
s Orbital
 These are spherical
 The probability of finding an electron depends on
the distance from the nucleus, not on direction
 There is only one possible orientation of a sphere:
mℓ = 0
 There is one s orbital per shell
 The size on the orbital increases as you go to a
higher shell
 Beyond the first shell, there are several regions of
maximum probability
s orbital
http://www.chemsoc.org/ExemplarChem/entries/2004/dublin_fowler/sorbitals
p Orbital
 These are dumbbell-shaped
 The electrons are distributed in identical lobes on
either side of the nucleus
 The lobes are separated by a nodal plane that cuts
through the nucleus
 When ℓ = 1, ml has three possibilities, one along
each axis
 As n increases, the size of the p orbital increases
p orbitals
px
py
pz
http://www.chemsoc.org/ExemplarChem/entries/2004/dublin_fowler/porbitals
d orbital
 These are found in the third and higher shells
 There are five d orbitals with two different shapes
 Four of them are clover-leaf shaped, having four
lobes of maximum probability and two nodal planes
 The fifth d orbital is dumbbell shaped along the z
axis with a donut region along the xy plane
 All five have the same energy
d orbitals
dz2
dx2-y2
http://www.chemsoc.org/ExemplarChem/entries/2004/dublin_fowler/dorbitals
d orbital
dxy
dxz
dyz
http://www.chemsoc.org/ExemplarChem/entries/2004/dublin_fowler/dorbitals
f orbitals
 There are seven f orbitals
 Each having eight lobes of maximum
electron probability separated by three nodes
 For hydrogen, the energy of an orbital is determined
by n
 For multi-electron atom, the energy level of the
orbitals depend on the shell as well as the subshells
 Within a given shell, the orbitals have slightly
different energies
 This is due to electron-electron repulsion
 As a result, outer shell electrons are shielded from
the effects of the nucleus by the inner shell
electrons
 The overall/net nuclear charge felt by an
electron is called the effective nuclear charge
Zeff and is lower than the actual nuclear
charge Z
 A lower angular momentum quantum
number corresponds to a higher Zeff and
therefore a lower energy level
Electronic Configuration
 Guided by a set of rules called the aufbau principles
 Rules of the aufbau principles
 Lower energy level orbitals are filled before higher energy
level orbitals
 An orbital can hold only two electrons, these two electrons
must have opposite spins (PAULI EXCLUSION
PRINCIPLE)
 For degenerate orbitals, one electron is placed in each orbital
(with the same spin quantum number), making them half
full, then the second electron is added
Hund’s Rule
 If two or more orbitals with the same energy
are available, one electron goes into each
until all are half-full. The electrons in the
half-filled orbitals all have the same value for
their spin quantum number.
Electron Configuration
 For carbon and nitrogen, the electrons are in
different p orbitals i.e. px, py, pz
 The singly occupied orbitals have the same value of
the spin quantum number +1/2 or –1/2
 Orbital filling diagrams are used to specify electron
configuration
 In these diagrams electron are represented as arrows
(pointing up or down)
 A single arrow indicates a half filled orbital while
an up and down pair indicate a full orbital
The Periodic Table
 The periodic table can be divided into four regions
or blocks of elements based on the orbitals being
filled
 Elements to the left: s block
 Elements in the middle: d block
 Elements to the right: p block
 The detached elements at the bottom are called
lanthanides and actinides, and these form the f
block elements
Periodic Table
Question
 Give the ground state electron configuration
of arsenic (Z = 33). Draw orbital filling
diagram, indicating the electron as up or
down.
Exercise
 Give the expected ground state electron
configuration for the following and draw
orbital filling diagrams for the first two
 Ti (Z = 22)
 Zn (Z = 30)
 Sn (Z = 50)
Exercise
 What is the likely ground state electron
configuration for the sodium ion Na+ formed
by loss of an electron from a neutral sodium
atom?
Anomalies with Electronic
Configuration
 There are a few anomalies concerning electronic
configuration
 Most of these anomalies usually occur in the elements with
atomic number greater than 40
 At this point the energy differences between the subshells
are small
 For example Cr and Cu
 An electron moves from a 4s to an energetically similar 3d
orbital
 A transfer in this way allows for decreased electron-electron
repulsion and therefore lowers the overall energy of the
atom
Electron Configuration of Ions
 Elements on the left side of the periodic table
(metals) tend to give up electrons to form cations
 Halogens and some other non-metallic elements
accept electrons to form anions
 Electrons given up by a metal come from the
highest energy occupied orbital
 The electrons accepted by a non-metal go to the
lowest energy occupied orbital
Electron Configuration of Ions
 Na: 1s2 2s2 2p6 3s1
 Na+: 1s2 2s2 2p6  Ne configuration
 Cl: 1s2 2s2 2p6 3s2 3p5
 Cl–: 1s2 2s2 2p6 3s2 3p6  Ar configuration
Electron Configuration of Ions
 For Main Group Elements
 All the elements in group 1A of the periodic table form
singly charged positive ions (cations) by losing one electron
 Likewise, the elements in group 2A form doubly positive
ions by losing two electrons
 The halogens in group 7A gain one electron to form singly
charged negative ions
 Group 6A non metals gain two electrons to form doubly
charged negative ions
Electron Configuration of Ions
 For transition metals
 These form cations by losing their valence s
electrons, then their d electrons
Mass Spectrometry
 Used to determine a compound’s molecular
formula by determining its molecular weight
 Mass spectrometer: an instrument used to
determine both atomic weight and molecular
weight
Mass Spectrometer
http://www.chemguide.co.uk/analysis/masspec/howitworks.html
Mass Spectrometry
 The sample is vaporized
 It is then injected (as a gas) into an evacuated chamber
 In this chamber, it is bombarded with a beam of high energy
electrons
 This beam of electrons is able to knock off other electrons
from the sample molecules making them positively charged
ions
 Ions of different masses are produced since some ionized
molecules fragment into smaller ions
 These different ions are accelerated by an electric field and
pass between the poles of a strong magnet
 As a result they are deflected through a curved pipe
Mass Spectrometry
 The radius of deflection depends on the mass of the ion
 Lighter ions are deflected more strongly than the heavier
ones
 Varying the strength of the magnetic field allows for
focusing of different ions through a slit and into a detector
 This gives rise to a mass spectrum results, which is a plot of
ion mass versus intensity (molecular weight of various ions
versus the relative number of ions produced)
 The heaviest ion is generally due to the ionized molecule
itself
 By determining the mass of this ion the molecular weight of
the molecule/compound can be determined
Mass Spectrum
http://www.chemguide.co.uk/analysis/masspec/howitworks.html
Exercise
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(a)Define the term atomic weight
A certain element has only two naturally occurring isotopes. One
isotope has an abundance of 57.3 % and isotoic mass of 120.904 amu.
Given that the atomic weight of the element is 121.757 amu,
determine the isotopic masss of the other isotope. What element is it
most likely to be?
(b) Briefly state the rules of the aufbau (building up) principle
(c) Draw the box and arrow diagram for the 3d, 4s and 4p orbitals of
the atom having the following electronic configuration:
[Ar] 3d10 4s2 4p2
Give the ground state electron configuration of the elements with the
following atomic numbers
(i) Z = 13
(ii) Z = 17
(iii) Z = 21
Exercise
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(a) On the basis of modern atomic theory, explain
what is meant by an atomic orbital.
(b) What three quantum numbers are used to
distinguish one atomic orbital from another and
what range of values is allowed for each quantum
number?
(c) Write the set of four quantum numbers for
each of the electrons in a ground state neon atom.
Exercise
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Write down the Balmer-Rydberg equation in
terms of whole numbers m and n.
Hence, given that the frequency of the emitted
light due to a transition from the n = 5 level to
amother level m is 2.969 x 1014 Hz, calculate the
value of m.
To which series of the atomic spectrum does the
transition belong?
Determine the energy of the radiation emitted.
Exercise
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(a)The quantum mechanical wave function, ψ, for electrons in atoms
is a function of n, ℓ and mℓ
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Write down the meaning of n, ℓ and mℓ.
List the possible values of n, ℓ and mℓ for all the electrons in Na+ and ClSketch the shape of the orbitals with l = 1 and l = 2.
(b) According to quantum mechanics the electron does not move in a
defined circular orbit around the nucleus. Briefly explain the quantum
mechanical view of the electron.
(c) Calculate the wavelength of the line with the longest wavelength
in the Lyman series of the hydrogen spectrum. (The Lyman series is
made up of electron transitions to the n = 1 level of the hydrogen
atom)