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**Electronic Structure of Atoms**

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**The Wave Nature of Light**

Electromagnetic radiation (EM radiation) carries energy through space. All EM radiation travels through a vacuum at 3.00 x 108 m/s (speed of light). You must memorize this number!!!

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Parts of a Light Wave Wave peak trough amplitude Wavelength (): distance between two wave peaks (m) Frequency (): number of waves per second. Units of Hertz (Hz) or reciprocal seconds (s-1). 1Hz = 1 s-1 Amplitude: half the distance from the wave peak to the trough.

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**What Is The Relationship Between Wavelength and Frequency?**

c = speed of light = 3.00 x 108m/s = wavelength (m) = frequency (s-1) nd are inversely proportional. As wavelength gets shorter, the frequency gets higher; as wavelength gets longer, the frequency gets lower.

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**Calculations With Wavelength and Frequency**

What is the wavelength of radiation with a frequency of 7.32 x 1019 s-1? What is the frequency of radiation having a wavelength of 754 nm?

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**Planck and Black-body Radiation**

Max Planck studied how temperature and EM radiation are related. He assumed energy can be emitted or absorbed by atoms only in discrete “chunks” of some minimum size. Quantum (“fixed amount”) is the smallest quantity of energy that can be absorbed or emitted as EM radiation.

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**Planck’s Equation E = energy of a single quantum (J)**

E = h E = energy of a single quantum (J) h = Planck’s constant: (6.626 x J-s) = frequency (s-1)

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**Using the Energy Equation**

Calculate the energy of light with a frequency of 6.00 x 1014 s-1.

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**More Energy Calculations**

Calculate the wavelength of light having an energy of 2.54 x J.

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**Planck’s Quantum Theory**

Energy is always absorbed or emitted in whole number multiples of hv (hv, 2hv, 3hv, etc.) Allowed energies are quantized = restricted to certain values. Planck’s theory applies best to small objects like electrons. Planck is “Father of Quantum Physics.”

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**Einstein and Photons Ephoton = hv or Ephoton = hc/λ**

Radiant energy striking a metal surface is a stream of tiny energy packets called photons. Photons behave like particles. The energy of a photon equals the frequency of light in which it travels. Ephoton = hv or Ephoton = hc/λ Radiant energy is quantized!

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**Einstein Discovered the Photoelectric Effect**

When a photon strikes a metal, it may transfer its energy to an electron. If the photon has enough energy to meet the electron’s specific energy requirement, the electron is emitted from the metal. Each metal has its own minimum energy needs to excite its electrons. This is called threshold energy. Not enough energy = no electron emission!

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**Radiant Energy and Spectra**

The radiant energy from a laser emits a single wavelength (monochromatic) but most common radiation sources such as light bulbs and stars emit many different wavelengths. A spectrum is produced when polychromatic radiation is separated into its different wavelengths. A spectrum producing light of all colors is called a continuous spectrum.

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**Line Spectra Not all radiation sources produce a continuous spectrum.**

When gases are placed in a tube under reduced pressure with high voltage, different colors of light are emitted. When light from such tubes are passed through a prism, only lines of a few wavelengths are seen. The colored lines are separated by black regions which correspond to absent wavelengths. These spectra are called line spectra.

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**Bohr’s Atomic Model Based On Spectral Lines**

Here is Bohr’s model of the hydrogen atom with electron movement corresponding to observed spectral lines.

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**Niels Bohr’s Atomic Model**

Bohr based his atomic model on the hydrogen atom with only one electron. He assumed that the electron moves in a circular orbit around the nucleus. According to classical physics, the electron should lose energy as it orbits and spiral into the nucleus. Since the electron does not spiral into the nucleus, the old laws of physics are inadequate to describe the atom.

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**Bohr’s Three Postulates**

Only orbits of certain radii with certain definite energies are permitted for electrons in an atom. An electron in a permitted orbit has a specific energy and is in an “allowed” energy state. It will not radiate energy and spiral into the nucleus. Energy is only emitted or absorbed by an electron as it changes from one energy state to another. Energy is emitted or absorbed as a photon (E = h).

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**Energy States of the Hydrogen Atom**

Integer n (values 1 to ) is called principal quantum number. Each n value corresponds to a different orbit. The radius of the orbit gets bigger as n increases. n = 1 is closest to the nucleus; succeeding n’s get farther away. The spacing between the n levels are uneven; the greatest spacing occurs between the nucleus and n = 1. Successive n levels are scrunched closer together. Lowest energy state is the ground state; a higher energy state is an excited state.

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**Significance of Bohr Model**

Works best for hydrogen atom; does not work well with mutli-electron atoms. Treats the electron as a small particle. Introduces distinct energy levels described by quantum numbers. Says that energy is needed to move an electron from one energy level to another.

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**Is Radiation a Particle or a Wave?**

Depending on experiment, radiation has either wavelike or particle-like (photon) character. Given that wavelengths of radiation have particle-like character, can matter (made up of particles) have wavelike character?

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**Wave-Particle Duality**

Louis de Broglie theorized that an electron in its movement about the nucleus does have a wavelength associated with it. Wave-particle duality: electrons have both particle and wave characteristics.

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**Heisenberg’s Uncertainty Principle**

It is impossible to know simultaneously both the exact momentum of an electron and its exact location. Leads to a new atomic model in which the energy of an electron is known but its location is described in terms of mathematical probabilities.

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**Quantum Mechanical Model**

Erwin Schrödinger uses an equation to incorporate the wavelike and particle-like qualities of electrons. This became the basis for the quantum mechanical (wave mechanical, electron cloud) model. This is our current atomic model!! Schrödinger’s work deals with probabilities.

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Schrodinger’s Model Probability density = the probability that an electron will be found at a given location. Node = a location where there is no probability of finding an electron. Electron density = region where there is a high probability of finding an electron.

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f-orbitals

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