Electrons in Atoms Big Idea #2 Electrons and the Structure of Atoms

Electrons in Atoms Big Idea #2 Electrons and the Structure of Atoms
Chemistry I Notes Ch. 5 Electrons in Atoms Big Idea #2 Electrons and the Structure of Atoms

What gives gas-filled lights their colors?
CHEMISTRY & YOU What gives gas-filled lights their colors? An electric current passing through the gas in each glass tube makes the gas glow with its own characteristic color. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Emission Spectra
Light has properties of both waves and particles. Light is a form of electromagnetic radiation – electric and magnetic fields oscillating at right angles to each other. Wave Characteristics Amplitude – height of wave from origin to peak (m) Wavelength -  -Distance between successive crests (m) Frequency –  - cycles per second (Hz) Speed – c- distance per unit time Light= 3x108 m/s Speed = frequency x wavelength c=  

Light and Atomic Emission Spectra
The Nature of Light By the year 1900, there was enough experimental evidence to convince scientists that light consisted of waves. The amplitude of a wave is the wave’s height from zero to the crest. The wavelength, represented by  (the Greek letter lambda), is the distance between the crests. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Nature of Light The frequency, represented by  (the Greek letter nu), is the number of wave cycles to pass a given point per unit of time. The SI unit of cycles per second is called the hertz (Hz). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The frequency () and wavelength () of light are inversely proportional to each other. As the wavelength increases, the frequency decreases. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Nature of Waves

Electromagnetic Waves
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The electromagnetic spectrum consists of radiation over a broad range of wavelengths. Low energy ( = 700 nm) High energy ( = 380 nm) Frequency  (s-1) 3 x 106 3 x 1012 3 x 1022 102 10-8 10-14 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Wavelength  (m)

Atomic Spectra cont… LIGHT: What Is It? Light Energy
Atoms As atoms absorb energy, electrons jump out to a higher energy level. Electrons release light when falling down to the lower energy level. Photons - bundles/packets of energy released when the electrons fall. Light: Stream of Photons

When atoms absorb energy, their electrons move to higher energy levels. These electrons lose energy by emitting light when they return to lower energy levels. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Atomic Spectra cont… Quantum – Restriction on the amount of energy an object emits or absorbs (Max Planck) E= h where E is the energy of a photon in joules (j) h is Planck’s constant 6.62x10-34 j-s  is the frequency in hertz (Hz) or 1/s Energies absorbed or emitted by atoms are quantized Photoelectric Effect- electrons ejected from the surface of a metal when light shines on it. For every metal there is a minimum frequency of light needed to release electrons. This quantum of energy is called a photon. (Albert Einstein) Thus light has particle wave duality

The energy absorbed by an electron for it to move from its current energy level to a higher energy level is identical to the energy of the light emitted by the electron as it drops back to its original energy level. The wavelengths of the spectral lines are characteristic of the element, and they make up the atomic emission spectrum of the element. No two elements have the same emission spectrum. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating the Wavelength of Light
Sample Problem 5.2 Calculating the Wavelength of Light Calculate the wavelength of the yellow light emitted by a sodium lamp if the frequency of the radiation is 5.09 × 1014 Hz (5.09 × 1014/s). Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown.
Sample Problem 5.2 1 Analyze List the knowns and the unknown. Use the equation c = ln to solve for the unknown wavelength. KNOWNS frequency (n) = 5.09 × 1014 /s c = × 108 m/s UNKNOWN wavelength (l) = ? m Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculate Solve for the unknown.
Sample Problem 5.2 2 Calculate Solve for the unknown. Write the expression that relates the frequency and wavelength of light. c =  Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.2 Calculate Solve for the unknown. 2 Rearrange the equation to solve for l. Solve for l by dividing both sides by n: = n c ln c = ln l = n c Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.2 Calculate Solve for the unknown. 2 Substitute the known values for n and c into the equation and solve.  = = = 5.89  10–7 m c  108 m/s   1014 /s Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Problem Calculate the wavelength of ultra violet light with a frequency of 2.00X1016 Hz?

Atomic Spectra cont… Types of spectra
Line Spectra – contain only specific wavelengths or colors – atoms emit these when their electrons are excited. Continuous Spectrum – white light broken into all its colors R-O-Y-G-B-I-V (rainbow) Absorption spectra – Black lines on the continuous spectra of star light that represent fingerprints of the elements present.

Refraction of White Light

The Line Spectrum of Hydrogen

The Quantum Concept and Photons
The Quantization of Energy German physicist Max Planck (1858–1947) showed mathematically that the amount of radiant energy (E) of a single quantum absorbed or emitted by a body is proportional to the frequency of radiation (n). E n or E = hn Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Quantization of Energy The constant (h), which has a value of  10–34 J·s (J is the joule, the SI unit of energy), is called Planck’s constant. E n or E = hn Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Photoelectric Effect Albert Einstein used Planck’s quantum theory to explain the photoelectric effect. In the photoelectric effect, electrons are ejected when light shines on a metal. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Photoelectric Effect Not just any frequency of light will cause the photoelectric effect. Red light will not cause potassium to eject electrons, no matter how intense the light. Yet a very weak yellow light shining on potassium begins the effect. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Photoelectric Effect To explain the photoelectric effect, Einstein proposed that light could be described as quanta of energy that behave as if they were particles. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Photoelectric Effect These light quanta are called photons. Einstein’s theory that light behaves as a stream of particles explains the photoelectric effect and many other observations. Light behaves as waves in other situations; we must consider that light possesses both wavelike and particle-like properties. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Photoelectric Effect No electrons are ejected because the frequency of the light is below the threshold frequency. If the light is at or above the threshold frequency, electrons are ejected. If the frequency is increased, the ejected electrons will travel faster. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Calculating the Energy of a Photon
Sample Problem 5.3 Calculating the Energy of a Photon What is the energy of a photon of microwave radiation with a frequency of 3.20 × 1011/s? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze List the knowns and the unknown.
Sample Problem 5.3 1 Analyze List the knowns and the unknown. Use the equation E = h × n to calculate the energy of the photon. KNOWNS frequency (n) = 3.20 × 1011/s h = × 10–34 J·s UNKNOWN energy (E) = ? J Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.3 2 Calculate Solve for the unknown. Write the expression that relates the energy of a photon of radiation and the frequency of the radiation. E = h n Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.3 2 Calculate Solve for the unknown. Substitute the known values for n and h into the equation and solve. E = h  = (6.626  10–34 J·s)  (3.20  1011/s) = 2.12  10–22 J Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Evaluate Does the result make sense?
Sample Problem 5.3 3 Evaluate Does the result make sense? Individual photons have very small energies, so the answer seems reasonable. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the frequency of a photon whose energy is 1.166  10–17 J?
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What is the frequency of a photon whose energy is 1.166  10–17 J?
E = h n n = h E  = = =  1016 Hz E  10–17 J h X 10–34 J·s Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Problem What is the energy of a photon of Infrared light with a wavelength of 1.00x10-5 m ? First calculate frequency using c=λv then calculate energy using E=hv

An Explanation of Atomic Spectra
The light emitted by an electron moving from a higher to a lower energy level has a frequency directly proportional to the energy change of the electron. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Quantum Mechanics The Wavelike Nature of Matter
Today, the wavelike properties of beams of electrons are useful in viewing objects that cannot be viewed with an optical microscope. The electrons in an electron microscope have much smaller wavelengths than visible light. These smaller wavelengths allow a much clearer enlarged image of a very small object, such as this pollen grain, than is possible with an ordinary microscope. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Quantum Mechanics Classical mechanics adequately describes the motions of bodies much larger than atoms, while quantum mechanics describes the motions of subatomic particles and atoms as waves. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Quantum Mechanics The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that it is impossible to know both the velocity and the position of a particle at the same time. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Quantum Mechanics The Heisenberg Uncertainty Principle
The Heisenberg uncertainty principle states that it is impossible to know both the velocity and the position of a particle at the same time. This limitation is critical when dealing with small particles such as electrons. But it does not matter for ordinary-sized objects such as cars or airplanes. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Quantum Mechanics To locate an electron, you might strike it with a photon. The electron has such a small mass that striking it with a photon affects its motion in a way that cannot be predicted accurately. The very act of measuring the position of the electron changes its velocity, making its velocity uncertain. Before collision: A photon strikes an electron during an attempt to observe the electron’s position. After collision: The impact changes the electron’s velocity, making it uncertain. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle? Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The Heisenberg uncertainty principle states that it is impossible to simultaneously know which two attributes of a particle? velocity and position Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Revising the Atomic Model
The Bohr Model of the Atom Electrons occupy specific energy levels in atoms. These energy levels are identified by a principle quantum number – n (1-7) When electrons occupy the lowest energy levels available the atom is in its ground state. When electrons occupy higher energy levels than the ground state the atom is in an excited state. When atoms absorb energy the electrons jump to higher energy levels (excited state). When they drop back down to the ground state these atoms emits light of specific wavelength corresponding to the energy change of the electron (emission spectra)

Energy Levels in Atoms The Bohr Model
Each possible electron orbit in Bohr’s model has a fixed energy. The fixed energies an electron can have are called energy levels. A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom. A person on a ladder cannot stand between the rungs. Similarly, the electrons in an atom cannot exist between energy levels. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The rungs on this ladder are somewhat like the energy levels in Bohr’s model of the atom. The energy levels in atoms are unequally spaced, like the rungs in this unusual ladder. The higher energy levels are closer together. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Revising the Atomic Model
Louis De Broglie (1924) proposed that particles of matter have wavelike character Heisenberg’s Uncertainty Principle – The position and speed of an electron cannot be measured simultaneously. If you measure one you can’t know the other. So electrons are located based on the probability of finding them in a region of space around an atom (orbital).

The Quantum Mechanical Model
Austrian physicist Erwin Schrödinger (1887–1961) used new theoretical calculations and experimental results to devise and solve a mathematical equation describing the behavior of the electron in a hydrogen atom. The modern description of the electrons in atoms, the quantum mechanical model, came from the mathematical solutions to the Schrödinger equation. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Like the Bohr model, the quantum mechanical model of the atom restricts the energy of electrons to certain values. Unlike the Bohr model, however, the quantum mechanical model does not specify an exact path the electron takes around the nucleus. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

The quantum mechanical model determines the allowed energies an electron can have and how likely it is to find the electron in various locations around the nucleus of an atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

In the quantum mechanical model, the probability of finding an electron within a certain volume of space surrounding the nucleus can be represented as a fuzzy cloudlike region. The cloud is more dense where the probability of finding the electron is high. Electron cloud Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Electron Arrangement in Atoms
Quantum Mechanical Model – Treats the electron as a wave with quantized energy and explains the behavior of atoms. Electrons occupy a cloud where the probability of finding an electron is highest where the cloud is densest. Orbitals – a region around the nucleus where an electron with a given amount of energy is likely to be found. Maximum capacity is 2 electrons.

Atomic Orbitals The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n). These numbers are assigned the values n = 1, 2, 3, 4, and so forth. For each principal energy level greater than 1, there are several orbitals with different shapes and at different energy levels. These energy levels within a principal energy level constitute energy sublevels. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Orbitals and Energy Electrons are found in primary energy levels sublevels and orbitals Primary energy level – quantum number n where n = 1-7 (floor of hotel) Sublevels – Each primary energy level has the number of sublevels equal to its n quantum number they are labeled s, p, d, & f (wing of hotel) s sublevels contain only 1 s orbital that can hold 2 electrons p sublevels contain 3 p orbitals that can hold 6 electrons d sublevels contain 5 d orbitals that can hold 10 electrons f sublevels contain 7 f orbitals that can hold 14 electrons

Orbitals and Energy cont…
Orbitals contain only 2 electrons s orbital – spherical shape 1 per energy level p orbital – dumbell shaped 3 per energy level d orbital – double dumbell shaped 5 per energy level f orbital – very complex shapes 7 per energy level Electrons within an orbital have opposite spin – Pauli Exclusion Principle

1s Orbital

The Boundary Surface Representations of All Three 2p Orbitals

The Boundary Surfaces of All of the 3d Orbitals

Representation of the 4f Orbitals in Terms of Their Boundary Surfaces

Orbital Energies

Electron Capacities of Shells and Orbitals
Primary energy Level 1 2 3 4 5 6 7 Orbital Type s s p s p d s p d f Electron Capacity 2 6 2 6 10 Total Electrons 8 18 32

Quantum Numbers and Electrons
If the primary energy level is given as n=1-7 Then the number of sublevels in that primary energy level = n The number of orbitals in that energy level = n2 The number of electrons in that energy level= 2n2

Calculate the maximum number of electrons in the 5th principal energy level (n = 5).
The maximum number of electrons that can occupy a principal energy level is given by the formula 2n2. If n = 5, 2n2 = 50. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

5.2 Electron Arrangement in Atoms cont…
Electron configurations are determined by distributing the atom’s electrons into energy levels, sublevels , and orbitals based on a set of principles. Aufbau Principle –Electrons are added one at a time to the lowest energy orbitals available until all electrons are accounted for. Pauli Exclusion Principle – Orbitals hold a maximum of 2 electrons with opposite spin. Hund’s Rule – Electrons occupy equal-energy orbitals so that a maximum number of unpaired electrons results (college dorm rule). Fill electrons into sublevels 1 per orbital until all orbitals have 1 then double up. Remember the exceptions at Copper and Chromium

Electron Configurations
Aufbau Principle According to the aufbau principle, electrons occupy the orbitals of lowest energy first. In the aufbau diagram, each box represents an atomic orbital. Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Aufbau Principle Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p The aufbau diagram shows the relative energy levels of the various atomic orbitals. Orbitals of greater energy are higher on the diagram. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Aufbau Principle Increasing energy 6s 5s 4s 3s 2s 1s 6p 5p 5d 4p 4d 4f 3p 3d 2p The range of energy levels within a principal energy level can overlap the energy levels of another principal level. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Pauli Exclusion Principle Spin is a quantum mechanical property of electrons and may be thought of as clockwise or counterclockwise. A vertical arrow indicates an electron and its direction of spin ( or ). An orbital containing paired electrons is written as . Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Hund’s Rule According to Hund’s rule, electrons occupy orbitals of the same energy in a way that makes the number of electrons with the same spin direction as large as possible. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Hund’s Rule Three electrons would occupy three orbitals of equal energy as follows. Electrons then occupy each orbital so that their spins are paired with the first electron in the orbital. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Look at the orbital filling diagram of the oxygen atom. An oxygen atom contains eight electrons. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Look at the orbital filling diagram of the oxygen atom. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 The 1s orbital has two electrons of opposite spin. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Look at the orbital filling diagram of the oxygen atom. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 The 1s orbital has two electrons of opposite spin. The 2s orbital also has two electrons of opposite spin. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Look at the orbital filling diagram of the oxygen atom. Each of the three 2p orbitals has one electron. The remaining electron now pairs with an electron occupying one of the 2p orbitals. Electron Configurations of Selected Elements Element 1s 2s 2px 2py 2pz 3s Electron configuration H 1s1 He 1s2 Li 1s22s1 C 1s22s22p2 N 1s22s22p3 O 1s22s22p4 F 1s22s22p5 Ne 1s22s22p6 Na 1s22s22p63s1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

A convenient shorthand method for showing the electron configuration of an atom involves writing the energy level and the symbol for every sublevel occupied by an electron. You indicate the number of electrons occupying that sublevel with a superscript. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

For hydrogen, with one electron in a 1s orbital, the electron configuration is written 1s1. For oxygen, with two electrons in a 1s orbital, two electrons in a 2s orbital, and four electrons in 2p orbitals, the electron configuration is 1s22s22p4. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

For hydrogen, with one electron in a 1s orbital, the electron configuration is written 1s1. For oxygen, with two electrons in a 1s orbital, two electrons in a 2s orbital, and four electrons in 2p orbitals, the electron configuration is 1s22s22p4. Note that the sum of the superscripts equals the number of electrons in the atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Writing Electron Configurations
Sample Problem 5.1 Writing Electron Configurations The atomic number of phosphorus is 15. Write the electron configuration of a phosphorus atom. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Analyze Identify the relevant concepts.
Sample Problem 5.1 Analyze Identify the relevant concepts. 1 Phosphorus has 15 electrons. There is a maximum of two electrons per orbital. Electrons do not pair up within an energy sublevel (orbitals of equal energy) until each orbital already has one electron. When writing electron configurations, the sublevels within the same principal energy level are written together. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Solve Apply the concepts to this problem.
Sample Problem 5.1 Solve Apply the concepts to this problem. 2 Use the aufbau diagram to place electrons in the orbital with the lowest energy (1s) first. 1s Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.1 Solve Apply the concepts to this problem. 2 Use the aufbau diagram to place electrons in the orbital with the lowest energy (1s) first. Continue placing electrons in each orbital with the next higher energy level. 1s 2s 2p 3p 3s 4s Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Sample Problem 5.1 Solve Apply the concepts to this problem. 2 Write the electron configuration. The electron configuration of phosphorus is 1s22s22p63s23p3. The superscripts add up to the number of electrons. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Exceptional Electron Configurations You can obtain correct electron configurations for the elements up to vanadium (atomic number 23) by following the aufbau diagram for orbital filling. If you were to continue in that fashion, however, you would assign chromium and copper the following incorrect configurations. Cr 1s22s22p63s23p63d44s2 Cu 1s22s22p63s23p63d94s2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Exceptional Electron Configurations The correct electron configurations are as follows: Cr 1s22s22p63s23p63d54s1 Cu 1s22s22p63s23p63d104s1 These arrangements give chromium a half-filled d sublevel and copper a filled d sublevel. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Exceptional Electron Configurations Some actual electron configurations differ from those assigned using the aufbau principle because although half-filled sublevels are not as stable as filled sublevels, they are more stable than other configurations. Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

What is the correct electron configuration of a sulfur atom?
A. 1s22s22p43s23p6 B. 1s22s22p63s23p3 C. 1s22s22p63s23p4 D. 1s22s22p63s63p2 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Energy Level Positions
For The First Twenty Elements 1S

Electrons in Atoms Big Idea #2 Electrons and the Structure of Atoms

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