# Chapter 5. Mendeleev s Periodic Table

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1 Chapter 5 Perodicity and Atomic Structure Mendeleev s Periodic Table In the 1869, Dmitri Mendeleev proposed that the properties of the chemical elements repeat at regular intervals when arranged in order of increasing atomic mass. Mendeleev is the architect of the modern periodic table. Chapter 5 2 1

2 Prediction of New Elements Mendeleev noticed that there appeared to be some elements missing from the periodic table so he left spots for undiscovered elements. Based on his periodic table, he accurately predicted the properties of some of these the unknown elements before their discovery. Chapter 5 3 Periodic Trends The arrangement of the periodic table means that the physical properties of the elements follow a regular pattern. Some trends include: Atomic Radius (end of Chapter 5) Ionization Energy (Chapter 6) Electron Affinity (Chapter 6) Electronegativity (Chapter 7) Chapter 5 4 2

3 The Structure of Atoms Plum Pudding Model Tootsie Pop Model Chapter 5 5 The Dual Nature of Light: The Particle and The Wave From the time of the ancient Greeks, people have thought of light as a stream of tiny particles - like marbles or billiard balls Thomas Young (in 1807) performed the now classic double slit experiment to test this theory. A great animation of the idea of light as waves and particles can be found here: Chapter

4 The Dual Nature of Light: The Wave As evidenced by the double slit experiment, light travels through space as a wave, similar to an ocean wave. Wavelength (λ) is the distance light travels in one cycle. Frequency (ν) is the number of wave cycles completed each second. Amplitude is the height measured from the center of the wave. The square of this value gives the Intensity. Velocity (c) = λ ν Light has a constant velocity (c) of m/s. Chapter 5 7 Frequency - Wavelength The red light in a laser pointer comes from a diode laser that has a wavelength of about 632 nm. What is the frequency of the light? Chapter 5 8 4

5 The Dual Nature of Light: The Particle In 1900, Max Planck proposed that radiant energy is not continuous, but is emitted as small bundles of energy This is the quantum concept. Planck determined that the energy of an emitted bundle is directly proportional to the frequency of the emitted light times a constant (h) E = hν = hc λ h = J s Chapter 5 9 The Photoelectric Effect The Photoelectric Effect shows that when light is shined on the surface of a metal, electrons are ejected and a current can be detected. Albert Einstein used Planck s idea of quanta to explain this phenomona. If the light were waves only, then the energy of that radiation would depend only on the intensity of the light. Einstein hypothesized that electrons are only ejected if the frequency of the light exceeds a threshold value specific to the metal, regardless of light intensity Even at low light intensities, electrons are ejected immediately if the frequency exceeds the threshold Millikan tested Einstein s hypothesis in 1914 and proved that is was correct Einstein wins the Nobel Prize! Yea! Chapter 5 10 Figure above from 5

6 Energy of Emission For red light with a wavelength of about 632 nm, what is the energy of a single photon and one mole of photons? Chapter 5 11 Wave Particle Duality Louis de Broglie suggested that if light can behave like matter (particles) then matter can behave as light. This concept is called wave particle duality. For a Particle E = mc 2 λ = h mv h = x kg m 2 / s For Light E = hν λ = h mc h = x J s Chapter

7 Wave Particle Duality How fast must an electron be moving if it has a de Broglie wavelength of 551 nm? How fast must an electron be moving if it has a de Broglie wavelength of 631 nm? m e = x kg Chapter 5 13 The Electromagnetic Spectrum The complete electromagnetic spectrum (all possible wavelengths and frequencies) is an un-interrupted band, or continuous spectrum. The radiant energy spectrum includes most types of radiation, most of which are invisible to the human eye. ROY G BIV Chapter

8 The Atomic Spectra When a particular element is heated and the light emitted is focused and passed through a prism, the resulting breakdown results in a non-continuous spectrum or a discrete line spectrum This spectrum is called the element s atomic spectrum The discrete lines indicate a light is emitted or absorbed in a series of discrete frequencies rather than continuously Each element has its own, unique spectrum Chapter 5 15 The Bohr Model of the Atom In 1913, Niels Bohr suggested a new model of the atom that explained why hydrogen had a discrete line spectrum rather than a continuous spectrum. Bohr's basic theory: electrons in atoms can only be at certain energy levels, and they can give off or absorb radiation only when they jump from one level to another. In his model that an atom consists of an extremely dense nucleus that is surrounded by electrons that travel in set orbits around the nucleus. He hypothesized that the energy possessed by these electrons and the radius of the orbits are quantized, meaning it is limited to specific values and is never between those values. These orbits were of varying energies, dependent on their distance from the nucleus The Gobstopper Model Chapter

9 Quantized versus Continuous The quantum concept means that the energy of the electron and its radius of orbit around the nucleus is limited to specific values (and cannot be anywhere in between!). If these values were continuous, they would be free to have any value. Energy E 3 hv = E 3 E 2 E 2 hv = E 3 E 1 hv = E 2 E 1 Chapter 5 E 1 17 Atomic Spectra: The Balmer-Ryberg Equation In 1885, Johann Balmer determined that the pattern of the atomic spectra of hydrogen could be predicted by a mathematical formula. Balmer determined that the wavelength or frequency of the lines in the spectrum could be expressed by the following equations: 1 E = R H ( n 2 i 1 - n 2 f ) R H is the Ryberg constant (2.18 x J) n i and n f are integers with n f > n i In addition to the lines seen in the visible region (Balmer series), there are additional sets of lines found in the UV region (Lyman series) and the IR region (the Paschen series). All conform to the above equations. Chapter

10 The Bohr Theory: Problems Bohr s theory only works for hydrogen atoms. Once you have more than one electron, the calculations for the electron energy and the orbit radii breakdown. Therefore, a new theory needed to be developed for multi-electron elements. Bohr s theory did make two important contributions: It suggested a reasonable explanation for the discrete line spectrum of the elements It introduced the idea of quantized electron energy levels (orbits!) Chapter 5 19 The Quantum Mechanical Model of the Atom In the 1920 s Erwin Schrödinger applied the principles of wave mechanics to atoms and developed the Quantum Mechanical Model of the Atom Basically, Schrödinger said to give up on the idea of literal orbits for the electrons and instead concentrate on the electron as a wave. This theory builds on Bohr s idea of quantized energy levels (orbits) and adds additional requirements for electron location and energy. Chapter

11 Quantum Mechanics Werner Heisenberg ( ): supported this idea by showing that it is impossible to know (or measure) precisely both the position and velocity (or the momentum) at the same time. The simple act of seeing an electron would change its energy and therefore its position. Think about pinpointing a fly on the wall. What happens when you try to swat it? h Heisenberg Uncertainty Principle :( x)( mυ) 4π h Uncertainty in electron's position :( x) (4π )( mυ) Chapter 5 21 Quantum Mechanics Working with Heisenberg s Principle, Schrödinger developed a compromise which calculates both the energy of an electron and the probability of finding an electron at any point in the molecule. This is accomplished by solving the Schrödinger equation, resulting in the wave function, Ψ. Wave Equation solve Wave Function or Orbital (Ψ) These regions were termed orbitals Probability of finding an electron in a region of space (Ψ 2 ) Chapter

12 Quantum Numbers The wave function contains three variables known as the Quantum Numbers which describe the size, energy, shape and position of the orbitals. n is the principal energy level (Bohr s Orbits!) l is the sublevel m l is the orbital These numbers serve as an address of the probable location of the electron. Chapter 5 23 Principal Quantum Number (n) The Principal Quantum Number (n) provides info about the distance of the electron from the nucleus As n increases, the number of allowed orbitals also increases as does the size of those orbitals. This increased size allows the electron to reside further from the nucleus As the electron moves away from the nucleus its energy increases, therefore n also indicates the energy of electrons We often state that electrons and orbitals denoted by the same n value are in the same shell Allowed Values: n = 1, 2, 3,... never 0 Chapter

13 Angular-Momentum Quantum Number (l) The angular momentum quantum number (l) defines the three dimensional shape of the orbitals found within a particular shell These discrete sets of orbitals are called sublevels The number of sublevels within a shell is equal to the principal quantum number (n) Allowed Values: l = 0, 1, 2... n - 1 l Value: Letter Used: s p d f Chapter 5 25 increasing energy Magnetic Quantum Number (m l ) The Magnetic Quantum Number (m l ) describes the orientation in 3D space of the sublevel, thereby denoting a specific orbital. The number of orientations (and therefore orbitals) per sublevel is determined by the equation: 2l + 1 Allowed Values: m l = - l,, + l l 0 (s) 1 (p) 2 (d) 3 (f) y axis 2l + 1 x axis Chapter 5 z axis 26 13

14 Spin Quantum Number (m s ) The Pauli Exclusion Principle states that no two electrons can have the same four quantum numbers This results in no more than double occupancy in any one orbital only two electron per orbital and they must have opposite spins Chapter 5 27 Electron Occupancy in Sublevels The Pauli Exclusion Principle states that an orbital can hold up to two electrons The maximum number of electrons in each of the sublevels depends on the number of orbitals within that sublevel: The s sublevel holds a maximum of 2 electrons (1 orbital). The p sublevel holds a maximum of 6 electrons (3 orbitals). The d sublevel holds a maximum of 10 electrons (5 orbitals). The f sublevel holds a maximum of 14 electrons (7 orbitals) The maximum electrons per principle quantum level (n) is obtained by adding the maximum number of electrons in each sublevel. Chapter

15 Quantum Number Combinations Why can t an electron have the following quantum numbers? (a) n = 2, l = 2, m l = 1 (b) n = 3, l = 0, m l = 3 (c) n = 5, l = 2, m l = 1 Give orbital notations for electrons with the following quantum numbers: (a) n = 2, l = 1, m l = 1 (b) n = 4, l = 3, m l = 2 (c) n = 3, l = 2, m l = 1 Chapter 5 29 Shapes of the Orbitals Each orbital has a specific shape determined by its angular momentum quantum number (l). As you increase the principle quantum number (n), the orbitals increase in size but not shape! Remember, these orbitals represent a region in space where there is a high probability of finding the electron. These are not discrete locations! They are also not pictures of the path that an electron follows around a nucleus Chapter

16 l = 0 : The s Orbitals The s orbitals are spherical, meaning the probability of finding the electron depends only on distance from the nucleus, not direction. The value of Ψ 2 is greatest near the nucleus then drops off as you move away. It never reaches zero however so there is technically no definite boundary to the atom. Chapter 5 31 l = 1 : The p Orbitals The p orbitals are dumbbell shaped with their electron density concentrated in identical lobes residing on opposite sides of a nodal plane. This shape means that a p electron will never be found near the nucleus. The two lobes of a p orbital have different phases (are opposite in sign) which becomes important in bonding among atoms. The three orientations (m l = -1, 0, +1) are 90 differentials along the x, y and z axes. The orbitals are designated p x (along the x axis), p y (along the y axis), and p z (along the z axis) Chapter

17 l = 2 : The d Orbitals Chapter 5 33 Effective Nuclear Charge (Z eff ) The nuclear charge (Z) of an atom is determined by the number of protons found in the nucleus It is felt by the electrons as an attraction Multiple electrons in an atom lead to a shielding effect on the outer electrons. This electron shielding (S) leads to energy differences among orbitals within a shell. Net nuclear charge felt by an electron is called the effective nuclear charge (Z eff ). Z eff = Z + S Chapter

18 Effective Nuclear Charge (Z eff ) Note that the 3d sublevel is actually higher in energy than the 4s sublevel. WHY?? Chapter 5 35 The Modern Periodic Table H.G.J. Moseley discovered that the nuclear charge increased by 1 for each element in the Mendeleev s table. He concluded that the changing atomic number rather than the changing mass explained the repeating trends of the elements The periodic law states that the properties of elements recur in a repeating pattern when arranged according to increasing atomic number. With the introduction of the concept of electron energy levels by Niels Bohr, the periodic table took its current arrangement. Chapter

19 Electron Configurations Many of an element s chemical properties depend on its electron configuration The electron configuration of an atom is a shorthand method of writing the location of electrons by sublevel. The principal quantum level (n) is written first, followed by the letter designation of the sublevel (l) then a superscript with the number of electrons in the sublevel. There are rules for the order and manner that each sublevel is filled called the Aufbau Principle. Chapter 5 37 Electron Configurations: Aufbau Principle Pauli Exclusion Principle: No two electrons in an atom can have the same quantum numbers (n, l, m l, m s ). Hund s Rule: When filling orbitals in the same sublevel, maximize the number of parallel spins (so fill then pair!). Rules of Aufbau Principle: 1. Lower n orbitals fill first. 2. Each orbital holds two electrons; each with different ms. 3. Half-fill degenerate orbitals before pairing electrons. Chapter

20 Using the Periodic Table for Electron Configurations The periodic table took on its current shape once the quantum model of the atom was developed. You can use it to fill up your sublevels and orbitals to build your electron configurations. Chapter 5 39 Writing Electron Configurations Step 1: Locate the element on the periodic table. Step 2: Determine the number of electrons the element has: Iron has 26 electrons Step 3: Starting at the beginning of the Periodic Table, move left to right across the periods, filling each sublevel with electrons until you reach the location of your element: Fe: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 Step 4: Check that the sum of the superscripts equals the atomic number of iron (26). Chapter

21 An Alternative Method Increasing Energy Core [He] [Ne] [Ar] [Kr] [Xe] [Rn] 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Chapter 5 41 Writing Electron Configurations Li 1s 2 2s 1 1s 2s Be 1s 2 2s 2 1s 2s B 1s 2 2s 2 2p 1 1s 2s 2p x 2p y 2p z C 1s 2 2s 2 2p 2 1s 2s 2p x 2p y 2p z Chapter

22 Writing Electron Configurations N 1s 2 2s 2 2p 3 1s 2s 2p x 2p y 2p z O 1s 2 2s 2 2p 4 1s 2s 2p x 2p y 2p z Ne 1s 2 2s 2 2p 5 1s 2s 2p x 2p y 2p z S [Ne] [Ne] 3s 2 3p 4 3s 3p x 3p y 3p z Chapter 5 43 Writing Electron Configurations Give the ground-state electron configurations for: Ne (Z = 10) Mn (Z = 25) Zn (Z = 30) Eu (Z = 63) W (Z = 74) Lw (Z = 103) Identify elements with ground-state configurations: 1s 2 2s 2 2p 4 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 6 1s 2 2s 2 2p 6 [Ar] 4s 2 3d 1 [Xe] 6s 2 4f 14 5d 10 6p 5 Chapter

23 Exceptions to the Filling Order When filling the d sublevel, exceptions occur for the chromium (Cr) and copper (Cu) families: 4s 3d 4p Cr 4s 3d 4p 4s 3d 4p Cu 4s 3d 4p Chapter 5 45 Periodic Trends The arrangement of the periodic table means that the physical properties of the elements follow a regular pattern. Some trends include: Atomic Radius (end of Chapter 5) Ionization Energy (Chapter 6) Electron Affinity (Chapter 6) Electronegativity (Chapter 7) Chapter

24 Atomic Radius An atom s atomic radius is the distance from the nucleus to the outermost electrons. Why do you think the radius increases in this way? Chapter

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