34 quantumnumbers
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The four quantum numbers describe the quantum mechanical properties of atomic orbitals. The principal quantum number (n) describes the main energy level or shell. The secondary quantum number (l) gives the sublevel or subshell and describes the shape of the orbital. The magnetic quantum number (ml) describes the orientation of an orbital in space. The spin quantum number (ms) describes the direction an electron is spinning and can have values of +1/2 or -1/2. Together, the four quantum numbers uniquely define the atomic orbital of an electron.
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This document provides an overview of chapter 2 from a foundation chemistry textbook. It covers the following topics:
- Atomic structure and the development of atomic models from Thomson to Bohr, including Rutherford's nuclear model and the dual nature of electrons.
- Quantum mechanics models of the atom including quantized energy levels, orbitals, and the four quantum numbers (n, l, ml, ms) that describe electrons.
- The shapes and orientations of s, p, d and f orbitals.
- Rules for writing electron configurations including the Aufbau principle and Hund's rule. Orbital diagrams are used to represent electron configurations.
- Partial orbital diagrams and condensed electron configurations are introduced
Atomic Structures - Dr. Mahbub.pptx
The document discusses the history of atomic structure theories including Dalton's, Thomson's, Rutherford's, Bohr's, and the quantum mechanical model. Dalton proposed that atoms are indivisible and compounds form by combination of atoms. Rutherford's gold foil experiment showed that the positive charge and mass of an atom are concentrated in a small nucleus. Bohr incorporated Planck's quantum theory, proposing electrons orbit in discrete energy levels. Later, the quantum mechanical model treated electrons as waves based on de Broglie's idea and Schrodinger's wave equation.
Quantum Numbers and Atomic Orbitals By solving t.pdf
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 no.ppt
The Electron Cloud Model describes an atom as consisting of a dense nucleus surrounded by electrons that exist in different probability clouds or regions at various energy levels, as developed by Erwin Schrodinger and Werner Heisenburg. The Heisenberg Uncertainty Principle states that it is impossible to know both the momentum and position of a particle like an electron at the same time. To measure an electron's position requires striking it with a photon, which affects its motion and makes its momentum uncertain. Quantum numbers describe an electron's unique state and include the principal, angular, magnetic, and spin quantum numbers.
Atomic structure part 2/3
Describe the Schroedinger wavefunctions and energies of electrons in an atom leading to the 3 quantum numbers. These can be also observed in the line spectra of atoms.
Atoms first chapter 3.7 11
This document discusses quantum theory and the electronic structure of atoms. It introduces quantum numbers like principal, angular momentum, and electron spin quantum numbers used to describe atomic orbitals. Atomic orbitals like s, p, and d orbitals are described along with their shapes and orientations. Electron configurations follow rules like the Aufbau principle, Pauli exclusion principle, and Hund's rule. The document shows how electrons fill atomic orbitals in order of increasing energy to write electron configurations of elements, which are represented using noble gas cores. Exceptions to electron filling order are noted for some transition metals.
95electrons in the same orbital have different rus values .docx
95
electrons in the same orbital have different rus values (one is +Yz and another -%),they
are said to be paired.
Electron Configuration
The energy of an electron in a hydrogen (H) atom is determined solely by its principal
quantum number n. However for many-electron atoms the orbital energies depend on
both the principal quantum number n andthe angular momenfum quantum number /.
Thus the energy of the orbitals in a many-electron atom increases in the order: ls < 2s <
2p < 3s a 3p < 4s < 3d < 4p < 5s, and so on. This order is also the order of filling
electrons into the orbitals in a many-electron atom. The guiding principle in assigning
electrons to the orbitals in a many-electron atom contains a set of three ru1es called the
Aufbau principle:
1. Lower-energy orbitals f,rll before higher-energy orbitals.
2. An atomic orbital can contain only two electrons, which must have opposite spins.
(Pauli exclusion principle: no two electrons in an atom can have the same four
quantum numbers.)
3 . When electrons are assigne d to p, d, or f orbitals, each successive electron enters a
different orbital of the subshell, each electron having the same spin as the previous
one; this proceeds until the subshell is half-full, after which electrons pair in the
orbitals one by one. (Hund's rule: the most stable arrangement of electrons in the
subshell is that with the maximum number of unpaired electrons, all with the same
spin.)
Flame Test
The resultant lowest-energy electron configuration is called the ground-state
configrnation of the atom. The electrons in the atom's outermost shell are called valance
electrons. When the atom absorbs enough energy, one or more of the valance electrons
move to a higher energy orbital, and the atom is said to be in an excited state. The excited
states are generally short-lived and rapidly decay back to the ground state by releasing
radiant energy in the form of light. The energy and frequency of the light that is released
during the decay transition depend on the difference in energy between the ground state
and the excited state. The energy difference (AQ, the frequency (v), and the wavelength
(2) of the light during emission are related by the equation, LE : hv: hclTwhere h ts
Planck's constant and c is the speed of light. When the wavelengths of the light emitted
fall in the visible region (400-800 nm), colors willbe observed.
Atoms of certain elements emit light
u'hen the elements or their
compounds are heated in a gas flame.
The flame takes on a distinctive
color detemined by the particular
element (flame test). Each atom has
its characteristic emission lines,
therefore flame tests can be used to
detect certain elements in unknown
cornpounds.
b!L
q)
Excited state
LE: hv: hclT
trl
Ground state
L
I
t
I
t
t
I
D
D
t
t
D
I
t
,
t
t
t
t
t
I
t
t
t
t
t
t
I
I
\ I
94
the energy of the electron increases, and the electron is farther away from the nucleus. A
coliection of orbitals with the same n is called an electr.
THE-QUANTUM-THEORY-QUANTUM-MECHANICS.pptx
This document provides an overview of the development of quantum theory models of the atom, including Rutherford's nuclear model, Bohr's model, de Broglie's proposal of the wave-like nature of electrons, Heisenberg's uncertainty principle, Schrodinger's equation, and the quantum numbers used to describe electron configuration. It introduces concepts like atomic orbitals, the Pauli exclusion principle, Hund's rule, and the Aufbau principle for building up electron configurations. Examples are provided to illustrate how to write electron configurations using quantum numbers and determine whether elements follow diamagnetism, paramagnetism, or the Pauli exclusion principle.
Atomic structure
This document summarizes key concepts in atomic structure:
1. It outlines the early theories of Dalton, Thomson, Rutherford, and Bohr, which proposed that atoms are made of fundamental particles and have small, dense nuclei surrounded by orbiting electrons.
2. It describes experiments that discovered the electron and properties of cathode rays. Rutherford's gold foil experiment provided evidence for a small, dense nucleus.
3. Quantum theory concepts like Planck's quantum hypothesis, Bohr's model of electron orbits, and de Broglie's matter waves are introduced along with equations relating wavelength, frequency and energy of photons.
Atom1
The document discusses several topics related to the electronic structures of atoms and electromagnetic radiation:
1. It defines wavelength and frequency of electromagnetic radiation and describes the relationship between them.
2. It discusses Max Planck's realization that energy is quantized and light has particle characteristics based on his study of blackbody radiation.
3. It explains Bohr's model of the hydrogen atom which incorporated Planck's quantum theory and correctly explained hydrogen's emission spectrum using discrete energy levels. However, the model failed for other elements.
Chemistry teaching
This presentation is about a brief description about the quantum numbers of chemistry that help to locate the position of an electron within an atom.
Atomic structure
- The atom consists of a small, dense nucleus surrounded by an electron cloud.
- Electrons can only exist in certain discrete energy levels around the nucleus. Their wavelengths are determined by the principal quantum number.
- The Bohr model improved on earlier models by introducing energy levels and quantization, but had limitations. The quantum mechanical model treats electrons as waves and uses Schrodinger's equation.
Chem I Day VIII
This document provides an overview of topics to be covered in Chemistry I class, including radioactive chemistry, half-life problems, isotopes, quantum numbers, the Heisenberg uncertainty principle, Schrodinger's wave equation, atomic orbitals, and an emission spectrum lab. It discusses converting between mass, moles, and number of particles. The class will review previous chapters, work on practice problems, and receive midterm grades.
Atomic structure presentation
This document defines various terms associated with elements and their subatomic particles. It then summarizes Rutherford's gold foil experiment and conclusions that led to the nuclear model of the atom. The document continues by describing the key subatomic particles (protons, neutrons, electrons), electromagnetic spectrum, photoelectric effect, atomic spectra, Bohr's model of the hydrogen atom, de Broglie wavelength, Heisenberg's uncertainty principle, Schrodinger wave equation, shapes of orbitals, filling of orbitals according to Aufbau principle and Hund's rule.
Chemistry-Presentation.pptx
The document discusses the quantum numbers used to describe electrons in atoms. There are four quantum numbers: principal (n), angular momentum (l), magnetic (ml), and electron spin (ms). The principal quantum number defines the electron's energy level and average distance from the nucleus. The angular momentum number describes the orbital shape as s, p, d, or f. The magnetic number defines the orbital orientation. Orbitals are regions where electrons are likely to be found and have different shapes depending on the angular momentum number.
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34 quantumnumbers
- 2. The Four Quantum Numbers • Quantum Numbers are numbers that describe the quantum mechanical properties of orbitals 1. The Principal Quantum Number (n) 2. The Secondary Quantum Number (l) 3. The Magnetic Quantum Number (ml) 4. The Spin Quantum Number (ms)
- 3. The Principal Quantum Number (n) • Gives the main energy level or shell • Describes the size and energy of an atomic orbital • n can have any integer value greater than zero n = 1, 2, 3, 4, …
- 4. The Secondary Quantum Number (l) • Gives the sublevel or subshell • Describes the shape of the orbital: • Sometimes called the ‘Angular Momentum Quantum Number’ • l can have any integer values from 0 to n-1 e.g. n l 1 0 2 0,1 3 0,1,2 4 0,1,2,3 • The energy of the orbital depends on l only in a multi-electron case; for electrons with the same n, energy of l=1 < l=2 < l=3… • Albert Michaelson worked with high resolution spectra and discovered that the lines in the hydrogen atom’s spectrum were actually made up of multiple smaller lines l = 0 1 2 3 s p d f
- 6. The Magnetic Quantum Number (ml) • Gives the exact orbital • Describes the orientation of an atomic orbital in space (how it lines up on the xyz plane) • ml can have integer values from –l to +l including 0 • The Zeemen effect showed that if a gas discharge tube was placed near a strong magnet some single lines in the spectrum split into new lines that were not initially present l ml 0 0 1 -1, 0, +1 2 -2, -1, 0, +1, +2 3 -3, -2, -1, 0, +1, +2, +3
- 7. So Far We Know This…
- 8. The Spin Quantum Number (ms) • Gives the spin state of the electron • Describes the direction in which the electron is spinning (identifies the electron within an orbital) • Goudsmit and Uhlenbeck noticed that an atom has a magnetic moment when it is placed in an external magnetic field • ms can have only two possible values: +1/2 or -1/2
- 9. The Pauli Exclusion Principle • In a given atom, no two electrons can have the same set of four quantum numbers (n, l, ml, and ms) • An orbital (same n, l, and ml) can hold a maximum of two electrons and they must have opposite spins (different ms)
- 10. In Summary
- 13. A Useful Formula
- 14. Applying the Four Quantum Numbers Energy
- 15. HOMEWORK Required Reading: p. 153-159 (remember to supplement your notes!) Questions: p. 159 #1-12