Properties of Light and Atomic Structure. Chapter 7. So Where are the Electrons? Electronic Structure of Atoms. The Wave Nature of Light!

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1 Properties of Light and Atomic Structure Chapter 7 So Where are the Electrons? We know where the protons and neutrons are Nuclear structure of atoms (Chapter 2) The interaction of light and matter helps us determine the electronic structure of atoms A. The wavelike nature of light B. Quantization C. The particle nature of light (photons) D. Bohr s model for the hydrogen atom E. The wavelike properties of the electron F. The quantum mechanical atom Electronic Structure of Atoms Understanding the electronic structure of atoms is the key to understanding the reactivity of elements and the reactions they undergo. Much of our knowledge of the electronic structure of atoms came from studying the ways elements absorb or emit light. To understand the interaction of light and matter, we need to understand the properties of light The Wave Nature of Light!

2 Wave A wave is a continuously repeating change or oscillation in matter or in a physical state Wave Properties Node time Wavelength W l h(λ (λ, lamda): peak to peak distance unit: m or nm Amplitude: maximum height of a wave Node: points of zero amplitude, occur at intervals of λ/2 Frequency (ν, nu): number of waves passing a given point per unit time unit: (s - ) or Hertz (Hz) Wavelength and Frequency Wavelength Frequency 2

3 Amplitude (Intensity) of a Wave Two waves with same wavelength and same frequency but different intensity! The Wave Nature of Light Light is a type of electromagnetic radiation - a form of energy with both electrical and magnetic components - propagates through space as oscillating electric and magnetic fields at perpendicular to each other Speed of light, c = x 0 8 ms - in vacuum Speed = wavelength x frequency or c = λ ν Wave-like Properties of Light Long wavelength Short wavelength Low-energy light High-energy light Different types of electromagnetic radiation have different properties because they have different ν and λ values. -Gamma rays (wavelength similar to diameter of atomic nuclei). -Hazardous -Radio waves (wavelength can be longer than a football field). -Safe 3

4 The Electromagnetic Spectrum Blue light has shorter wavelength than red light Blue light has higher frequency than red light Blue light more energetic than red light Speed of light: x 0 8 ms - = c = λ ν λ ν E Infrared Radiation The Electromagnetic Spectrum Speed of light: x 0 8 ms - = c = λ.ν Convert wavelength to frequency: blue light, 420. nm Α. ν =7.4 x 0-4 s - B. ν = 7.4 x 0 4 s - C. ν = x 0 4 s - D. ν = x 0-4 s - What is the color (i.e. λ) of the light of a frequency of 4.22 x 0 4 s - a. λ = 70. nm red b. λ = 560. nm yellow c. λ = 520. nm green d. λ = 450. nm indigo 4

5 The Particle Nature of Light Blackbody Radiation and Quantization of Energy The spectrum of radiation given off by a heated object Classical physics: vibrating atoms in the heated object emit radiation and all frequencies of radiations are allowed Modern (quantum) physics: vibrating atoms emit radiation but only certain frequencies are allowed (quantized) Planck s Equation A ball rolling down a ramp versus stairs Classical: Ramp Quantized: Stairs Energy of a these allowed frequencies are given by c E = hν = h λ h = Planck s constant = 6.63x0-34 Joule. Second = 6.63x0-34 J.s Photoelectric Effect Ejection of electrons when light strikes the surface of a metal Minimum energy required to eject an electron Number of electrons ejected is measured as electrical current Low frequency light High frequency light Low intensity High intensity Low intensity High intensity 5

6 Vending machine Photon Analogy 00 ping-pong balls at mile per hour or golf ball at 00 miles per hour Photoelectric Effect Some key results For low frequency light Electrons are not ejected regardless of the light s intensity For high frequency light Same number of electrons are ejected regardless of the frequency Increasing the light s intensity increases the current Quantized Energy and Photons Einstein explained these results of photoelectric effect by assuming that the light striking the metal is a stream of tiny massless energetic particles (photons). The energy of each photon is proportional to its frequency. E = hν When a photon strikes a metal surface, energy is transferred to the electrons in the metal. If the energy of the photon is higher, the electron can overcome the attractive forces holding it to the metal. If the frequency of the light is higher than critical frequency, the extra energy simply increases the kinetic energy of the ejected electrons. 6

7 Quantized Energy and Photons Einstein s explanation of the photoelectric effect led to a conclusion that light have both wave-like and particle-like properties. Photon Energy What s the energy of each photon of blue light? Of red light? Of a mole of photons? Calculate the energy of a photon of yellow light whose wavelength is 589 nm. Atomic Models Bohr model This model is based on our understanding of the solar system Quantum mechanical model This model is based on our understanding of probabilistic nature of matter comprising atomic system 7

8 Atomic Emission Spectra Why would an atom emit only certain frequencies of light and not all of them? Atomic Emission Spectra The hydrogen spectrum correlates with a mathematical relationship called Rydberg equation λ =R - when n > n 2 R (Rydberg constant) =.0974 x 0 7 m - Atomic Emission Spectra The hydrogen spectrum correlates with a mathematical relationship called Rydberg equation λ =R - when n > n 2 R (Rydberg constant) =.0974 x 0 7 m - For n=3, λ = Α. 656 nm, red B. 486 nm, green C. 434 nm, blue D. Α mixture of 656, 486, and 434 i.e. white 8

9 Atomic Emission Spectra The hydrogen spectrum correlates with a mathematical relationship called Rydberg equation λ =R - when n > n 2 R (Rydberg constant) =.0974 x 0 7 m - For n=5, λ = Α. 656 nm, red B. 486 nm, green C. 434 nm, blue D. Α mixture of 656, 486, and 434 i.e. white Atomic Emission Spectra The hydrogen spectrum correlates with a mathematical relationship called Rydberg equation λ =R - when n > n 2 R (Rydberg constant) =.0974 x 0 7 m - For n=4, λ = Α. 656 nm, red B. 486 nm, green C. 434 nm, blue D. Α mixture of 656, 486, and 434 i.e. white Atomic Emission Spectra Calculation of emission lines for H λ =R - when n > n 2 R (Rydberg constant) =.0974 x 0 7 m - n = 3, λ = x 0-7 m or nm = red line n = 4, λ = x 0-7 m or nm = green line n = 5, λ = x 0-7 m or nm = blue line 9

10 The Bohr Model of the Atom Electrons move in circular orbits around the nucleus. There exist discrete steps in the spread of the energy of electrons. Only certain orbits are allowed (quantized). n in the Rydberg equation refers to different allowed orbits. As n increases the radius of the orbit increases. An electron in a permitted orbit has a specific energy (an allowed energy state, energy is quantized). The Bohr Model of the Atom The energy of the orbit is lowest for n= and increases with increasing n. Light emitted as electron moves from higher E orbit (excited state) to lower E orbit (ground state) and light absorbed as electron moves from lower E orbit to higher E orbit. Energies of Allowed Orbits For n=2, Ε = Α J/atom B J/atom C J/atom 0

11 Energies of Allowed Orbits For n=, Ε = Α J/atom B J/atom C J/atom Energies of Allowed Orbits For n=3, Ε = Α J/atom B J/atom C J/atom The Bohr Theory and the Spectra of Excited Atoms Light emitted as electron moves from higher E orbit (excited state) to lower E orbit (ground state) and light absorbed as electron moves from lower E orbit to higher E orbit.

12 Transition Energies Energy absorbed n = n = 2 Wavelength of absorbed light Interaction of Light and Matter absorbed light emitted light The same energy light is absorbed and emitted absorbed light emitted light Lower energy light is emitted than absorbed How Many Absorptions? A B C

13 How Many Emission Lines? A B C Why Are Objects Colored? Corresponds to λ = 300 nm Corresponds to λ = 500 nm Not colored colored Energy levels for the H-atom in the Bohr model 3

14 The Bohr model effectively explains the line spectra of atoms and ions with a single electron H, He +, Li 2+ What about more complex atoms or ions? Quantum mechanical model 4

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