Electrons in Atoms

1. Electrons in Atoms Chapter 5

2. Light and Quantized Energy Section 5.1

3. Objectives • Compare the wave and particle models of light. • Define a quantum of energy and explain how it is related to an energy change of matter. • Contrast continuous electromagnetic spectra and atomic emission spectra.

4. Recall . . . • Rutherford’s nuclear atomic model • All of an atom’s positive charge and almost all of its mass are concentrated in a central structure called the nucleus. • Fast-moving electrons are found in the space surrounding the nucleus.

5. Unanswered Questions • Rutherford’s atomic model was incomplete. • Why weren’t the negatively charged electrons pulled into the positively charged nucleus? • How were electrons “arranged” around the nucleus? • How does the model explain differences in chemical behavior between elements?

6. More Unanswered Questions • In the early 1900’s, scientists found that certain elements emitted visible light when heated in a flame. Different elements emitted different colors of light. • Analysis of the emitted light revealed that this chemical behavior is related to the arrangement of electrons in an element’s atoms. Fluorine Copper

7. Understanding the Nature of Light • Wave Nature of Light • Electromagnetic radiation is a form of energy that exhibits wavelike behavior as it travels through space. • Different types of EM radiation include radio waves, microwaves, X rays, and visible light (also called sunlight or white light). • All forms of EM radiation can be depicted in an electromagnetic spectrum.

8. The Electromagnetic Spectrum See pg. 139 in text

9. Wave Characteristics • Notice (from the EM spectrum) that each type of radiation has a characteristic wavelength and frequency. • Wavelength and frequency, along with amplitude and speed, are 4 characteristics common to all waves.

10. Wave Characteristics • Wavelength, represented by the symbol λ (lambda), is the length of 1 wave. It is defined as the distance between equivalent points on a continuous wave. • Generally, wavelength is measured crest to crest or trough to trough.

11. Wave Characteristics • Wavelength (cont.) • The units for wavelength are units of distance - m, cm, or nm. • Amplitude is the height of a wave from its origin to its crest (or trough).

12. Wave Characteristics • Frequency, represented by the symbol ν (nu) or ƒ, is the number of waves that pass a given point in a unit of time. • Hertz (Hz), the SI unit for frequency, equals 1 wave per second. • In calculations, frequency is expressed with the units “waves per second” where “waves” is accepted as understood. Frequency is in 1/s or s-1. 82 Hz = 82 waves/second = 82/s = 82 s-1

13. Wave Characteristics • All electromagnetic waves travel at a speed of 3.00 x 108 m/s in a vacuum. This is often referred to as “the speed of light” even though it refers to all EM waves. • The symbol for the speed of light is c. • Mathematically, the speed of light is the product of its wavelength and its frequency or C = λν(C = λf)

14. C = λν (C=λf) • Wavelength and frequency are inversely proportional. • This means, that if the wavelength increases, the frequency has to decrease (and vice versa). • If a type of EM radiation has a long wavelength, its frequency must low. If it has a short wavelength, its frequency is high.

15. Practice Problems • What is the frequency of green light, which has a wavelength of 4.90 x 10-7 m? • An x ray has a wavelength of 1.15 x 10-10m. What is its frequency? • What is the speed of an electromagnetic wave that has a frequency of 7.8 x 106 Hz? • What is the wavelength of a microwave having a frequency of 3.44 x 109 Hz?

16. White Light • Let’s look closer at sunlight. Remember, it is a type of EM radiation. • Sunlight (and all EM radiation) contains a continuous range of wavelengths and frequencies. • A prism will separate white light into a continuous spectrum of colors. • The colors of the visible spectrum are ROYGBIV.

17. White Light • The visible spectrum (as well as the EM spectrum) is a continuous spectrum because every part of it corresponds to a unique λ and ν. • Each color then corresponds to a particular wavelength & frequency.

18. White Light • Red light has a relatively long λ and low frequency while violet light has a short λ and a high frequency. • Energy increases with frequency. Therefore violet light has more energy than red light (or yellow or green).

19. Wave Model of Light • Much evidence supports the idea that light, or any EM radiation, is a form of energy that travels through space as a wave. This is the “wave model" of light. • This model does not explain all of light’s characteristics: • Why do hot objects emit only certain frequencies of light? (see Fig. 6 p. 141) • Why do certain metals emit electrons when certain colors of light hit them (called the photoelectric effect)? (see Fig. 7 p. 142) • Why do elements emit distinctive colors of light when burned? (see photos p. 907)

20. The Particle Nature of light • Max Planck (1858-1947) searched for an explanation for the color of light emitted from heated objects. • The temperature of an object is a measure of the average kinetic energy of its particles. • As an object got hotter, it emitted different colors of light. • Different colors correspond to different wavelengths and, therefore, different frequencies of light.

21. Quantum/Quanta • Max Planck concluded that matter can gain energy only in small, specific amounts called quanta. A quantum is the minimum amount of energy that can be gained or lost by an atom. • Therefore, objects increase in temperature in small steps as they absorb quanta of energy • Since the steps are so small, the temperature increase seems continuous.

22. An Analogy Quanta • Think of each quantum of energy as a step in a staircase. • To walk up the staircase, you move up one step at a time. You do not move up a 1/2 step or 1 1/2 steps. • When an object increases in energy, it increases 1 quantum at a time. 4 3 2 1 0

23. The Particle Nature of Light • Planck said the light energy emitted by hot objects is quantized - it is emitted in quantum units of energy. • He showed that the energy emitted is related to the frequency of the light through this equation: Equantum = hν (Eq = hf) • h is called Planck’s constant and is equal to 6.626 x 10-34 J-s (J stands for joule) • ν(or f) is the frequency in s-1

24. E = hν (E = hf) • This equation shows that matter can emit or absorb energy only in whole number multiples of hν- quantities of energy between these values does not exist. • This equation could explain the photoelectric effect as well as the color changes of objects as they heat up. • The photoelectric effect is when electrons are emitted from a metal’s surface when light of a certain frequency shines on it.

25. The Photoelectric Effect • According to the wave model, any color light should cause the emission of “photoelectrons” from a metallic surface. • It was observed, however, that the light had to be of a minimum frequency (or higher) to cause the photoelectric effect.

26. The Particle Nature of light • In 1905, Albert Einstein combined Planck’s idea of quantized energy with the wave nature of light and proposed the Dual Theory of Light. • He proposed that light is composed of tiny bundles of energy (called photons) that behave like particles but travel in waves. • A photon is a particle of EM radiation with no mass that carries one quantum of energy.

27. Photons • Einstein said that a photon’s energy would depend on its frequency. He modified Planck’s equation: Ephoton = hf • Einstein proposed that there is a minimum or threshold frequency that a photon of light must have to cause ejection of photoelectrons. Photons below that frequency would not have enough energy to cause photoelectron ejection. • High frequency violet light causes electron emission while red light does not.

28. (E = hf Practice Problems h = 6.626 x 10-34 J-s) • What is the energy of a photon of violet light that has a frequency of 7.23 x 1014 s-1? • What is the frequency of a photon of EM radiation that has 6.29 x 10-20 J of energy? • What is the energy of EM radiation having a frequency of 1.05 x 1016 s-1?

29. Atomic Emission Spectra • The light of a neon sign is produced by passing electricity through a tube filled with neon gas. • Neon atoms absorb energy and become excited. They are unstable. • Unstable atoms release the energy as light (to stabilize themselves.) • If the light emitted is passed through a prism, a series of colored lines are produced. See Fig. 8, p. 144

30. Atomic Emission Spectra

31. Atomic Emission Spectra • The atomic emission spectrum of an element is the set of frequencies of the electromagnetic waves emitted by atoms of the element. • An AES consists of individual lines of color - it is NOT continuous. • An AES is also referred to as a bright line or line spectra.

32. Atomic Emission Spectra • Each atom has a unique AES. (see next slide) • The elements of an unknown compound can be identified by using the AES of known elements. • A flame test is a large scale version of an AES and is used as a quick way to make identifications. Fluorine

33. Hydrogen Mercury Helium

34. Atomic Emission Spectra • The fact that only certain colors appear (as lines) in an element’s spectrum means that only certain specific frequencies of light are emitted. • Those frequencies can be related to energy by the formula: Ephoton = hv. • The conclusion is that only photons having certain specific energies are emitted from “excited” atoms.

35. Photons