Electrons in Atoms Chapter 5

Light and Quantized Energy Section 5.1 Rutherford proposed that all of an atom’s positive charge and virtually all of its mass are concentrated in the nucleus that is surrounded by fast-moving electrons. His model did not account for the differences in chemical behavior among the various elements. An element’s chemical behavior is related to the arrangement of the electrons in its atoms.

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.

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.

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?

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

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. See pg. 139 in text. Visible light is a type of electromagnetic radiation. Other types: Microwaves that warm and cook X rays Radio and television waves.

The Electromagnetic Spectrum

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.

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. Wavelength (λ) is the shortest distance between equivalent points on a continuous wave. Frequency (υ) is the number of waves that pass a given point per second. One hertz (Hz), the SI unit of frequency, equals one wave per second. Amplitude of a wave is the wave’s height from the origin to a crest, or from the origin to a trough.

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).

82 Hz = 82 waves/second = 82/s = 82 s-1 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

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 = λf Because the speed of light is such an important and universal value, it is given its own symbol. Although the speed of all electromagnetic waves is the same, waves may have different wavelengths and frequencies. They are inversely related, as one goes up the other goes down.

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.

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? 3.00 x 108 m/s

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.

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.

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).

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?

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.

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 The steps are so small the temperature increase seems continuous.

An Analogy Think of each quantum of energy as a step in a staircase. 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

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 = hf h is called Planck’s constant and is equal to 6.626 x 10-34 J-s (J stands for joule) f is the frequency in s-1

E = hf This equation shows that matter can emit or absorb energy only in whole number multiples of hf - 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.

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.

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.

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.

(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?

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

Atomic Emission Spectra

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.

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

Hydrogen Mercury Helium Visible spectrum is continuous (on the top) Each element’s spectrum consists of several individual lines of color.

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.

Photons