Chapter 7: Electronic Structure Electrons in an atom determine virtually all of the behavior of the atom. Quantum theory – the study of how energy and matter interact on an atomic level. To understand the electron, we must first understand light. Reason =

Light Also known as electromagnetic radiation. Ex) Visible light, Infrared, X-ray, Radio. All electromagnetic radiation have several common characteristics. ◦ Light as a wave ◦ Light as a particle ◦ “Duality of Light”

Electromagnetic Radiation

Light as a Wave Wavelength ( – lambda) = Frequency ( – nu) =

Light as a Wave Wavelength and Frequency are inversely related.

Electromagnetic Spectrum Shows the full range of electromagnetic radiation that exists.

Light as a Wave The product of the wavelength and the frequency, though, is a constant. c = , where c is the speed of light. Thus, if we know the frequency, we can find the wavelength and vice versa. LEP #1(a).

Proof of Waves Waves exhibit certain properties when they interact with each other. Young’s Double Slit experiment.

Proof of Waves

Light as a Particle The wave nature of light does not explain all of the properties of light. Blackbody radiation – when solids are heated, they will glow. Color depends on the temperature.

Light as a Particle Max Planck – proposed a theory that energy from blackbody radiation could only come in discrete “chunks” or quanta. E = h h = x J  s LEP #1(b).

Light as a Particle The photoelectric effect (Einstein) also is proof that light must have a tiny mass and thus act as a particle (photon). LEP #2, #3.

Line Spectra When a gas like H 2, Hg, or He is subjected to a high voltage, it produces a line spectrum consisting of specific wavelengths.

Line Spectra

High Voltage Excitation

Identifying Metals Na = yellow K = violet Li = red Ba = pale green

Line Spectra The four lines for hydrogen were found to follow the formula: Where the values of n are integers with the final state being the smaller integer.

Bohr Theory How could such a simple equation work? Niels Bohr some thirty years later came up with a theory. Classic physics would predict that an electron in a circular path should continuously lose energy until it spiraled into the nucleus.

Bohr Theory 1. An electron can only have precise energies according to the formula: E = -R H / n 2 ; n = 1, 2, 3, etc. and R H is the Rydberg constant. 2. An electron can travel between energy states by absorbing or releasing a precise quantity of energy.

Bohr Theory

Can not explain the line spectra for other elements due to electron-electron interactions. Thus, the formula for Hydrogen can only be applied for that atom. LEP #4.

Matter as a Wave Louis de Broglie proposed that if light could act as both a wave and a particle, then so could matter. Where h is Planck’s constant, m is the objects mass, and v is its velocity. Size, though, matters. LEP #5.

Matter as a Wave De Broglie was later proven correct when electrons were shown to have wave properties when they pass through a crystalline substance. Electron microscope picture of carbon nanotubes.

Uncertainty Principle German scientist Werner Heisenberg proposed his Uncertainty Principle in History

Uncertainty Principle For a projectile like a bullet, classic physics has formulas to describe the motion – velocity and position – as it travels down range.

Uncertainty Principle Any attempt to observe a single electron will fail.

Uncertainty Principle If you want to measure length, there is always some uncertainty in the measurement. To improve the certainty, you would make a better measuring device. Heisenberg, though, stated that the precision has limitations.  x  m  v  h / 4 

Uncertainty Principle Once again, size makes a big difference. LEP #6

Uncertainty Principle Determinacy vs. Indeterminacy According to classical physics, particles move in a path determined by the particle’s velocity, position, and forces acting on it ◦ determinacy = definite, predictable future Because we cannot know both the position and velocity of an electron, we cannot predict the path it will follow ◦ indeterminacy = indefinite future, can only predict probability

Uncertainty Principle

Quantum Mechanics The quantum world is very different from the ordinary world. Millions of possible outcomes and all are possible! Quantum Café “I am convinced that He (God) does not play dice.” Albert Einstein

H  = E  Erwin Shrödinger proposed an equation that describes both the wave and particle behavior of an electron. The mathematical function, , describes the wave form of the electron. Ex) a sine wave. Squaring this function produces a probability function for our electron.

Atomic Orbitals A graph of  2 versus the radial distance from the nucleus yields an electron “orbital”. An “orbital” is a 3D shape of where an electron is most of the time. An “orbital” can hold a maximum of two electrons.

Atomic Orbitals The Probability density function represents the probability of finding the electron.

Atomic Orbitals A radial distribution plot represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases

Atomic Orbitals The net result for the Hydrogen electron is a most probable distance of 52.9pm.

Atomic Orbitals For n=2 and beyond, the orbital will have n-1 nodes. A node is where a zero probability exists for finding the electron.

Atomic Orbitals  2s orbital = 1 node 3s orbital = 2 nodes 

Quantum Numbers An electron can be described by a set of four unique numbers called quantum numbers. 1. Principle quantum number, n = describes the energy level of the electron. As n increases so does the energy and size of the orbital. n can have values of integers from 1 to infinity.

Quantum Numbers 2. Azimuthal quantum number, l, defines the shape of the orbital. The possible values of l depends on n and can be all of the integers from 0 to n-1. However, the values of 0, 1, 2, and 3 have letter designations of s, p, d, and f, respectively.

Quantum Numbers 3. Magnetic quantum number, m l describes the orientation in space of the orbital. The possible values of this quantum number are – l  0  + l. When l is not zero, the magnetic q.n. has more than one value. These multiple values produce degenerative orbitals – orbitals of equal energy.

Quantum Numbers 4. Spin quantum number, m s describes the electron spin of the electron. This value is either +1/2 or –1/2.

Quantum Numbers

Pauli Exclusion Principle – no electron in an atom can have the same set of four quantum numbers. Ne = 10 electrons LEP #7.

Subshell Designations Value of l 0123 Type of orbital spdf

Orbitals s type orbitals are spherical in shape.

Orbitals p type orbitals have two lobes.

Orbitals d type orbitals generally have four lobes.