In this presentation you will be able to, describe how atomic orbitals arise from the Schrodinger's equation, relate orbital shapes to electron density distribution and interpret the information obtained from a four set of quantum numbers.
Hello! I've created this PowerPoint presentation as a requisite in General Chemistry 1 subject during SY 2019–2020.
Electronic Structure of Atoms
- Quantum Mechanical Description of Atom
- Schrödinger’s Model of Hydrogen Atom and Wave Functions
- Main Energy Levels, Sublevels, and Orbitals
- Quantum Numbers
- Electron Configuration
Should you need a .pptx file, kindly email me at rd.chrxlr@gmail.com.
An easy guide to one of the most important principles taught in secondary chemistry, The Aufbau Principle. Helpful for students who consider such an amazing topic to be a nightmare. Happy Chemistry!
Welcome! I make this slide for students of gcse Edexcel.
content of the slides:
1. Compare the size of nanoparticles with the sizes of atoms and molecules.
2. Describe how the properties of Nano particulate materials are related to their uses including surface area to volume ratio of the particles they contain, including sunscreens.
3. Explain the possible risks associated with some Nano particulate materials
Compare, using data, the physical properties of glass and clay ceramics, polymers, composites and metals.
4. Explain why the properties of a material make it suitable for a given use and use data to select materials appropriate for specific uses
Properties of periodic table by Saliha RaisSaliha Rais
The presentation "Properties of Periodic Table" is prepared for grade IX students. The slide show includes a brief description on the properties of elements in the periodic table, that shifts periodically, hence explaining the concept of periodicity. the main topics include Atomic Radii, Ionization energy, Electron affinity and Electronegativity.
Every physical phenomenon in the Physics world involves some sort of attractions and repulsions and make the world exist in a special form. It is because of attraction and repulsions between particles that the environment remains in a well-equipped and well balanced environment. Copy the link given below and paste it in new browser window to get more information on Coulomb’S Law www.askiitians.com/iit-jee-electrostatics/coulombs-law/
Hello! I've created this PowerPoint presentation as a requisite in General Chemistry 1 subject during SY 2019–2020.
Electronic Structure of Atoms
- Quantum Mechanical Description of Atom
- Schrödinger’s Model of Hydrogen Atom and Wave Functions
- Main Energy Levels, Sublevels, and Orbitals
- Quantum Numbers
- Electron Configuration
Should you need a .pptx file, kindly email me at rd.chrxlr@gmail.com.
An easy guide to one of the most important principles taught in secondary chemistry, The Aufbau Principle. Helpful for students who consider such an amazing topic to be a nightmare. Happy Chemistry!
Welcome! I make this slide for students of gcse Edexcel.
content of the slides:
1. Compare the size of nanoparticles with the sizes of atoms and molecules.
2. Describe how the properties of Nano particulate materials are related to their uses including surface area to volume ratio of the particles they contain, including sunscreens.
3. Explain the possible risks associated with some Nano particulate materials
Compare, using data, the physical properties of glass and clay ceramics, polymers, composites and metals.
4. Explain why the properties of a material make it suitable for a given use and use data to select materials appropriate for specific uses
Properties of periodic table by Saliha RaisSaliha Rais
The presentation "Properties of Periodic Table" is prepared for grade IX students. The slide show includes a brief description on the properties of elements in the periodic table, that shifts periodically, hence explaining the concept of periodicity. the main topics include Atomic Radii, Ionization energy, Electron affinity and Electronegativity.
Every physical phenomenon in the Physics world involves some sort of attractions and repulsions and make the world exist in a special form. It is because of attraction and repulsions between particles that the environment remains in a well-equipped and well balanced environment. Copy the link given below and paste it in new browser window to get more information on Coulomb’S Law www.askiitians.com/iit-jee-electrostatics/coulombs-law/
Quantum Numbers and Atomic Orbitals By solving t.pdfarasanlethers
Quantum Numbers and Atomic Orbitals By solving the Schrödinger equation (Hy
= Ey), we obtain a set of mathematical equations, called wave functions (y), which describe the
probability of finding electrons at certain energy levels within an atom. A wave function for an
electron in an atom is called an atomic orbital; this atomic orbital describes a region of space in
which there is a high probability of finding the electron. Energy changes within an atom are the
result of an electron changing from a wave pattern with one energy to a wave pattern with a
different energy (usually accompanied by the absorption or emission of a photon of light). Each
electron in an atom is described by four different quantum numbers. The first three (n, l, ml)
specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can
occupy that orbital. Principal Quantum Number (n): n = 1, 2, 3, …, 8 Specifies the energy of
an electron and the size of the orbital (the distance from the nucleus of the peak in a radial
probability distribution plot). All orbitals that have the same value of n are said to be in the same
shell (level). For a hydrogen atom with n=1, the electron is in its ground state; if the electron is in
the n=2 orbital, it is in an excited state. The total number of orbitals for a given n value is n2.
Angular Momentum (Secondary, Azimunthal) Quantum Number (l): l = 0, ..., n-1. Specifies the
shape of an orbital with a particular principal quantum number. The secondary quantum number
divides the shells into smaller groups of orbitals called subshells (sublevels). Usually, a letter
code is used to identify l to avoid confusion with n: l 0 1 2 3 4 5 ... Letter s p d f g h ... The
subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and so on. The
value of l also has a slight effect on the energy of the subshell; the energy of the subshell
increases with l (s < p < d < f). Magnetic Quantum Number (ml): ml = -l, ..., 0, ..., +l. Specifies
the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the
subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell.
Thus the s subshell has only one orbital, the p subshell has three orbitals, and so on. Spin
Quantum Number (ms): ms = +½ or -½. Specifies the orientation of the spin axis of an electron.
An electron can spin in only one of two directions (sometimes called up and down). The Pauli
exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same
atom can have identical values for all four of their quantum numbers. What this means is that no
more than two electrons can occupy the same orbital, and that two electrons in the same orbital
must have opposite spins. Because an electron spins, it creates a magnetic field, which can be
oriented in one of two directions. For two electrons in the same orbital, the spins must be
opposite to each oth.
Quantum mechanical model of atom belongs to XI standard Chemistry which describes the quantum mechanics concept of atom, quantum numbers, shape and energies of atomic orbitals.
BOHR ATOM MODEL - BOHR SOMERFIELD MODEL - de-BROGLIE DUAL NATURE OF ATOM - SCHRODINGER WAVE EQUATION -MODERN PERIODIC LAW - ELECTRONEGATIVITY SCALES - SLATER RULE - BALANCING OF REDOX EQUATIONS
At the end of this chapter you should be able to sketch the periodic table showing the groups and periods; identify the metals, metalloids and non-metals in the periodic table. Identify the representative elements, the transition elements, the transition metals, the lanthanides and actinides in the periodic table. Also, give the electron configuration of cations and anions; determine the trends in the physical properties of elements in a group; describe and explain the trends in atomic properties in the periodic table; compare the properties of families and elements; predict the properties of individual elements based on their position in the periodic table; and perform exercises and collaborative work with peers.
What is tetrahedron,a trigonal bipyramid, and an octahedron? In this lesson you will be able to: apply the valence shell electron pair repulsion theory to predict the molecular geometry of simple molecules; define dipole moment; predict the polarity of molecules.
This would enable students to explain the emission spectrum of hydrogen using the Bohr model of the hydrogen atom; calculate the energy, wavelength, and frequencies involved in the electron transitions in the hydrogen atom; relate the emission spectra to common occurrences like fireworks and neon lights; and describe the Bohr model of the atom and the inadequacies of the Bohr model.
According to Gilbert Lewis, atoms combine i order to achieve a more stable electron configuration. Maximum stability is obtained when an atom is isoelectronic with a noble gas. This presentation would enable students to relate lattice energy with physical properties such as melting point.
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
2. Explain Heisenberg’s Uncertainty Principle
Describe how atomic orbitals arise from the
Schrodinger equation
Relate orbital shapes to electron density
distribution
Qualitatively sketch the orbital shapes
Interpret the information obtained from a set of
four quantum numbers
Objectives
3. Assign the correct set of quantum numbers
for an electron
Objectives
4. a. Heisenberg’s Uncertainty Principle
b. Schrodinger Equation
c. Wave function
d. Electron probability density
e. Atomic orbital
f. Principal quantum number
g. Angular momentum quantum number
Keywords
6. HEISENBERG’S UNCERTAINTY
PRINCIPLE
formulated by Werner Heisenberg, a German
physicist
“the position of a particle and its momentum
cannot be simultaneously measured with
arbitrarily high precision”
In other words, it is not possible to measure
the exact position and the exact momentum
of a particle at the same time.
7. Mathematically, this is stated as:
where "x is the uncertainty in position, "p is
the uncertainty in momentum, and h is
Planck’s constant
8. The Bohr model violates Heisenberg’s
Uncertainty Principle. Electrons do not go
around the nucleus in well-defined orbits.
Otherwise, we will be able to determine the
exact position and momentum of the electron
in the atom at the same time.
A better model is needed to fully describe the
atom.
9. SCHRODINGER EQUATION
In 1926, Erwin Schrodinger, an Austrian
physicist, formulated a mathematical equation
that describes the behavior and energies of
submicroscopic particles.
The Schrodinger equation incorporates
particle behavior and wave behavior, treating
the electron as a standing wave.
10. SCHRODINGER EQUATION
The solution to the Schrodinger equation is a
wave function called ψ (psi). The wave
functions are also called atomic orbitals (as
distinguished from the Bohr orbits). Aside
from the wave functions, energies are also
obtained from solving the equation.
11. The wave function itself has no physical
meaning. However, the probability of finding
the electron in a particular volume element in
space is proportional to ψ2. In wave theory,
the intensity of light is proportional to the
square of the amplitude of the wave or ψ2.
Similarly, the most likely place to find the
particle is where the value of ψ2 is greatest.
12. The Schrodinger equation began a new field in
physics and chemistry referred to as quantum
mechanics or wave mechanics.
The Schrodinger equation can be solved exactly
for the hydrogen atom but not for atoms with
more than one electron. For many-electron
atoms, approximation methods are used to
solve the Schrodinger equation.
13. THE QUANTUM MECHANICAL
DESCRIPTION OF THE HYDROGEN ATOM
It is not possible to pinpoint the exact location
of the electron in an atom but ψ2 gives the
region where it can most probably be found.
The electron density gives the probability that
the electron will be found in a particular
region of an atom.
14. THE QUANTUM MECHANICAL
DESCRIPTION OF THE HYDROGEN ATOM
representation of the electron density
distribution around the nucleus in the
hydrogen atom
15. THE QUANTUM MECHANICAL
DESCRIPTION OF THE HYDROGEN ATOM
The darker the shade, the higher the
probability of finding the electron in that
region.
the probability distribution is spherical
ψ is the solution to the Schrodinger equation.
It is also referred to as an atomic orbital.
16. THE QUANTUM MECHANICAL
DESCRIPTION OF THE HYDROGEN ATOM
When we say that the electron is in an atomic orbital,
we mean that it is described by a wave function, ψ,
and that the probability of locating the electron is
given by the square of the wave function associated
with that orbital.
The atomic orbital has a characteristic energy as well
as a characteristic electron density distribution. This
electron density distribution in three-dimensions
gives the shape of the atomic orbital.
17. In the mathematical solution of the Schrodinger
equation, three quantum numbers are obtained.
These are the principal quantum number (n), the
angular quantum number, (ℓ) ,and the magnetic
quantum number (ml). They describe the atomic
orbitals. A fourth quantum number, the spin
quantum number (ms) completes the description
of the electrons in the atoms.
The QUANTUM NUMBERS
18. a. Determines the energy of an orbital
b. Determines the orbital size
c. Is related to the average distance of the electron from
the nucleus in a particular orbital; the larger the n
value, the farther the average distance of the electron
from the nucleus
d. Can have the values: n = 1, 2, 3, …
e. Orbitals with the same n are said to be in the same
shell.
Principal Quantum Number (n)
19. a. Describes the “shape” of the orbitals
b. Can have the following values: ℓ = 0, 1, 2, up to n-1.
Examples
n value ℓ value
1 0
2 0, 1
3 0, 1, 2
Angular Momentum Quantum Number
(ℓ)
20. c. Orbitals with the same n and ℓ values belong
to the same subshell.
d. It is usually designated by letters s, p, d, f, …
which have a historical origin from spectral
lines. The designations are as follows
Angular Momentum Quantum
Number (ℓ)
21. The s, p, d, f designations of the orbitals refer
to sharp, principal, diffuse, and fundamental
lines in emission spectra.
22. a. Describes the orientation of the orbital in
space
b. Can have the values: - ℓ, (-ℓ + 1), … 0, … (+ ℓ -
1), + ℓ
Magnetic Quantum Number
(ml)
23. a. The first three quantum numbers describe
the energy, shape and orientation of
orbitals. The 4th quantum number refers to
two different spin orientations of electrons
in a specified orbital.
Electron Spin Quantum
Number (ms)
24. b. When lines of the hydrogen spectrum are
examined at very high resolution, they are
found to be closely spaced doublets and
called as the Zeeman effect. This splitting is
called fine structure, and was one of the first
experimental evidences for electron spin. The
direct observation of the electron's intrinsic
angular momentum was achieved in the
Stern–Gerlach experiment.
Electron Spin Quantum
Number (ms)
25. Electron Spin Quantum
Number (ms)
c. Uhlenbeck, Goudsmit, and Kronig (1925)
introduced the idea of the self-rotation of
the electron. The spin orientations are called
"spin-up" or "spin-down" and is assigned
the number ms = ½ ms = -½, respectively.
26. d. The spin property of an electron would give
rise to magnetic moment, which was a
requisite for the fourth quantum number.
The electrons are paired such that one spins
upward and one downward, neutralizing the
effect of their spin on the action of the atom
as a whole. But in the valence shell of atoms
where there is a single electron whose spin
remains unbalanced, the unbalanced spin
Electron Spin Quantum
Number (ms)
27. creates spin magnetic moment, making the
electron act like a very small magnet.
The four quantum numbers compose the
numbers that describe the electron in an atom.
The quantum numbers shall be in the order:
energy level (n), sub-level or orbital type (ℓ), the
orientation of the orbital specified in ℓ (mℓ), and
the orientation of the spin of the electron (ms). It
is written in the order (n, ℓ, mℓ, ms).
Electron Spin Quantum
Number (ms)
28. 1. An electron is found in the first energy level.
What is the allowed set of quantum numbers
for this electron?
2. What is the total number of orbitals
associated with the principal quantum
number n=1?
3. What is the total number of orbitals
associated with the principal quantum
number n=2?
Example
29. 4. What is the total number of orbitals
associated with the principal quantum
number n=3?
5. List the values of n, ℓ , mℓ for an orbital in the
4d subshell.
30. What are the shapes of the atomic orbitals?
• Strictly speaking, an orbital does not have a
definite shape because the wave function
extends to infinity. However, while the electron
can be found anywhere, there are regions
where the probability of finding
it is much higher.
The Representations of the
Shapes of Atomic Orbitals
31. The Representations of the
Shapes of Atomic Orbitals
The electron density distribution of a 1s electron
around the nucleus.
32. The p orbitals starts when n =2 for which ℓ has a
value of 1 and mℓ has values -1, 0, +1. There are
three 2p orbitals: 2px, 2py, 2pz indicating the axes
along which they are oriented. For the p
orbitals, the electron probability density is not
spherically symmetric but has a double teardrop
shape, or a dumbbell shape. The greatest
probability of finding the electron is within the
two lobes of the dumbbell region;
The Representations of the
Shapes of Atomic Orbitals
33. it has zero probability along the nodal planes found
in the axes. All three 2p orbitals are identical in
shape and energy but differ in orientation.
The Representations of the
Shapes of Atomic Orbitals
34. The d orbitals occur for the first time when n = 3.
The angular function in these cases possesses
two angular (or planar) nodes. Four of the
orbitals have the same basic shapes except for
the orientation with respect to the axes. The
wave functions exhibit positive and negative
lobes along the axes and shows zero probability
of finding the electron at the origin.
The Representations of the
Shapes of Atomic Orbitals
35. The fifth wave function,
dx2 , has a similar
shape with that
of the p-orbital
with a donut-shape
region along the x-axis.