Periodicity and Atomic Structure

UU chem 216 chapter 5

Development of the periodic table

• The most important organizing principle in chemistry (1869). It explained known facts and made predictions about unknown phenomena, elements and their properties.

• Periodicity – the repeating of various traits like atomic radii and valence electrons.

• Mendeleev’s chart lacked the Noble gases, which were discovered in 1984.

Light and the electromagnetic spectrum

• Studies of the interaction of radiant energy with matter have provided immense insight into atomic and molecular structure.

• Electromagnetic spectrum: chart of all the different kind of electromagnetic energy from gamma rays to radio waves.

• Duality of light: in a vacuum (space) travels like waves with a frequency, wavelength and amplitude and carries energy as discrete units called a photon.

Electromagnetic wave

• Wave direction perpendicular to the fields

Calculating a frequency from a wavelength

• Wavelength X frequency = speed• Lamda λ (m) v (s-1) c (m/s)• The light blue glow given off by mercury

streetlamps has a wavelength of 436 nm. What is its frequency in hertz?

Electromagnetic energy and atomic line spectra

• sunlight is white light which is a continuous distribution of wavelengths of the entire visible spectrum.

• When shone through a glass prism, the different wavelengths travel at different rates and the wavelengths are separated. This is what happens in rainbow and parhelion (sundog)

• http://micro.magnet.fsu.edu/primer/java/scienceopticsu/newton/index.html

The dispersion of visible light

Atomic line spectra

• Atoms give off light when heated or energetically excited giving clue to their atomic makeup.

• Light excited contain only a few wavelengths rather than a full rainbow, giving a series of discrete lines on dark background – line spectrum with each element have its own unique spectral “signature / pattern.” Johann Balmer (series) visible. Johannes Ryndberg made fit all

• Lyman series – spectral lines in ultraviolet region• Paschen, Brackett, and Pfund – in infared region

Spectrum pictures

• Wavelength Color 656.2 red 486.1 blue-green 434.0 blue-violet 410.1 violet

Balmer – Rydberg equation

• 1/λ =R[1/m2-1/n2] or v=R*c[1/m2-1/n2]• λ - wavelength• R(Ryndberg constant) = 1.097 x 10-2nm-1 • M and n represent integers with n>m. If m=1,

then Lyman series, m=2 then Balmer, if m=3 the Paschen series.

Calculation using Balmer – Rydberg

• What are the two longest – wavelength (nm) in the Lyman series of the hydrogen spectrum? n=2, n=3.

• What is the shortest – wavelength line (nm) in the Lyman series of the hydrogen spectrum? n=infinity

Particlelike properties of electromagnetic energy

• Albert Einstein - photoelectric effect- irradiating a clean metal surface with light causes electrons to be ejected from the metal, with a threshold value different for each metal.

• The beam of light behaves as it were a stream of particles (photons) whose energy (E) is related to their frequency, v (or wavelength λ ) by equation E=hv or hc/λ

• Higher frequencies and shorter wavelength correspond to higher energy radiation (lower frequency and longer wavelength, lower energy)

Photoelectric effect

Quantum

• Intensity of light beam measures the number of photon, frequency measure of energies.

• Light / matter are quantized – both occur only in discrete amount, like steps vs a ramp.

• Neils Bohr- his model the energy levels of the orbits are quantized

Calculating the energy of a photon from its frequency

• What is the energy (kJ / mole) of photons of radar waves with a v of 3.35 x 108 Hz

Wavelike properties of matter

• Louis de Broglie (1892-1987) if light can behave in some respects like matter, then perhaps matter can behave in some respects like light / particles

• He substituted Einstein E=mc2 into the λ =hc/E to his equation of λ = h/mv

• The dual wave / particle description of light and matter is really just a mathematical model. We can’t see atoms and observe their behavior directly.

Standing wave review

Calculating the De Broglie wavelength of a moving object

• What is the de Broglie wavelength (meters) of a pitched baseball with a mass of 120g and a speed of 100 mph (44.7 m/s)?

De Broglie electron• Wavelike pattern for electron

Quantum mechanic and the Heisenberg Uncertainty principle

• Erwin Schrodinger -1926- proposed the quantum mechanical model, electron -wavelike not particle like (orbits)

• Werner Heisenberg – it is impossible to know exactly where an electron is and what path it follows. By seeing, energy is imparted to make it move faster and thus change its position. Not know both position and velocity. If mass is large enough, Heisenberg relationship too small to show problem measuring mass and velocity.

• (delta X) (Delta mv) > h/ 4 pi

Using the Heisenberg Uncertainty principle

• Assume that you are traveling at a speed of 90 km/h in a small car with a mass of 1250 kg. If the uncertainty in the velocity of the car is 1% (delta v = 0.9 km/h) what it the uncertainty (in meters) in the position of the car? How does this compare to electron (300pm, size / diameter is 240 pm)

Wave function and Quantum number

• Schrodinger’s quantum mechanical model is a differential equation called a wave equation, since similar to fluid waves. Solution to equation is called wave functions or orbitals, represented by Greek psi (Ψ ). Square of wave function is probability of finding the electron within a specific region. A wave function is characterized by three parameters called quantum numbers represented by letters n, l, m which describe the energy levels of the orbitals and 3-D shape of the region of space.

Psi squared

Quantum numbers

• The principal quantum number is (n) is a positive integer which size and energy primary dependent, shells around nucleus.

• The angular – momentum quantum number (l) defines the 3-D shape of the orbital. If N=1, then l = 0, If N=2, then l= 0 or 1, if N=2, then l= 0,1,2 . Orbitals within a shell is grouped into subshell. 0=s, 1=p, 2=d, 3=f,

Electron spin and the Pauli Exclusion Principle

• Magnetic quantum number (ml) defines the spatial orientation of the orbital in respect to a set or coordinate axes. For the value of l, there are 2l +2 different spatial orientation.

• If l= 0, then ml= 0, if l=1, the ml = -1, 0, +1; If l=2, then ml = -2,-1,0,+1,+2

• Spin quantum number (ms)- +1/2 ( )or -1/2 ( ) Electrons closely paired, spin opposite. Independent of other 3.

• Wolfgang Pauli exclusion principle– no two electrons can have the same 4 quantum number.

Quantum numbers

The shape of orbitals• S orbitals – spherical – distance dependent, not

direction, only 1 s subshell per shell. Size increases in higher shells, Within is a spherical node – zero probability. No planar node

• P orbitals – dumbbell – shaped, identical lobes on the either side of a planar node. 3 orbitals at 90* angles along the x, y, and z axes.

• D orbitals – four clover leaf and 1 dumbbell in a doughnut. 2 nodal planes

• F orbitals – 7 f orbitals with 8 lobes separated by 3 nodal planes

• http://www.youtube.com/watch?v=sMt5Dcex0kg

Orbital shapes

Quantum mechanics and atomic line spectra

• When electron absorbs energy from a flame or electronic discharge they jump to a higher energy level. It is unstable, so it rapidly returns to a lower-energy level along with emission of energy equal to the difference of the higher to lower level. We observed the emission of only specific frequencies of radiation, color wavelengths.

Calculating the energy difference between two orbitals

• What is the energy difference (kJ / mol) between the first and second shells of the hydrogen atom if the lowest-energy mission in the Lyman series occurs at λ = 121.5 nm?

Orbital energy levels in Multielectron atom

• Many different interaction for multielectron as compare to hydrogen with only 1 electron.

• Repulsion of outer-shell electrons by inner-shell election.

• The nuclear charge felt by an electron if the effective nuclear charge, Zeff.

• Zeff = Zactual – Electron shielding• The inner electrons shield the outer electrons

from the full charge of the nucleus.

Electron shielding

Electron configurations of multielectron atoms

• Predict which orbitals are occupied by electrons. 3 Rules called the Aufbau (building up) principle guides the filling order of orbitals. The resultant lowest energy is called the ground- state electron configuration. Several orbitals will have the same energy-level which are said to be degenerate.

Rules of Aufbau principle

• 1. Lower-energy orbitals fill before higher-energy orbits.

• 2. An orbital can hold only 2 electrons, which must have the opposite spins. (Pauli exclusion)

• 3. If 2 or more degenerate orbitals are available, one electron goes into each until all are half – full (Hund’s rule-far apart due to repulsion

• List n quantum number and the s,p,d,f beginning with lowest energy and showing the occupancy of orbital as superscript.

Some anomalous electron configurations

• Due to the unusual stability of both half-filled and fully filled subshells.

• Chrominum – predict [Ar] 4s23d4 actually [Ar] 4s13d5

• Copper – predict [Ar] 4s23d9 actually has [Ar]4s13d10

• Most anomalous elements occur in elements with atomic numbers greater than z=40, where energy differences are small.

Common anomalous configurations

• Element Predicted Electron Configuration Actual Electron Configuration

• copper, Cu [Ar] 3d9 4s2 [Ar] 3d10 4s1 • silver, Ag [Kr] 4d9 5s2 [Kr] 4d10 5s1 • gold, Au [Xe] 4f14 5d9 6s2 [Xe] 4f14 5d10 6s1 • palladium, Pd [Kr] 4d8 5s2 [Kr] 4d10 • chromium, Cr [Ar] 3d4 4s2 [Ar] 3d5 4s1 • molybdenum, Mo [Kr] 4d4 5s2 [Kr] 4d5 5s1

Electron configurations and the periodic table

• All element in a group have similar valence-shell electron configurations.

• Groups 1A,2A form s- block• Groups 3A-8A form the p-block• Transitional elements form the d block• Rare earth (lanthanide /actinide) – form the f

block• 1s-2s-2p-3s-3p-4s-3d-4p-5s-4d-5p-6s-4f-5d-6p-

7s-5f-6d-7p

Periodic table and quantum numbers

Electron configuration arrow diagram

Assigning a ground-state electron configuration to an atom

• Give the ground-state electrons configuration of arsenic, z=33, and draw and orbital filling diagram, indicating the electrons as up or down arrows.

• Identify the atom with the following ground-state electron configuration

• [Kr] ___ ___ ___ ___ ___ ___ ___ ___ __

Electron configurations and periodic properties: atomic radii

• Size or atomic radius can be predicted by electron configuration

• Define an atom’s radius as being half the distance between the nuclei of two identical atoms when they are bonded together.