chemistry help

chapter7.3.pdf

Home >Chemistry homework help >chemistry help

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 1/10

The Photoelectric Effect

Einstein arrived at this conclusion through his analysis of the photoelectric effect (for which he later was awarded the Nobel Prize). The photoelectric effect refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it. The following observations characterize the photoelectric effect.

1. Studies in which the frequency of the light is varied show that no electrons are emitted by a given metal below a specific threshold frequency, .

2. For light with frequency lower than the threshold frequency, no electrons are emitted regardless of the intensity of the light.

3. For light with frequency greater than the threshold frequency, the number of electrons emitted increases with the intensity of the light.

4. For light with frequency greater than the threshold frequency, the kinetic energy of the emitted electrons increases linearly with the frequency of the light.

Chemical Connections

Fireworks

The art of using mixtures of chemicals to produce explosives is an ancient one. Black powder—a mixture of potassium nitrate, charcoal, and sulfur—was being used in China well before 1000 A.D. and has been used subsequently through the centuries in military explosives, in construction blasting, and for fireworks. The du Pont Company, now a major chemical manufacturer, started out as a manufacturer of black powder. In fact, the founder, Eleuthère du Pont, learned the manufacturing technique from none other than Lavoisier.

Before the nineteenth century, fireworks were confined mainly to rockets and loud bangs. Orange and yellow colors came from the presence of charcoal and iron filings. However, with the great advances in chemistry in the nineteenth century, new compounds found their way into fireworks. Salts of copper, strontium, and barium added brilliant colors. Magnesium and aluminum metals gave a dazzling white light. Fireworks, in fact, have changed very little since then.

How do fireworks produce their brilliant colors and loud bangs? Actually, only a handful of different chemicals are responsible for most of the spectacular effects. To produce the noise and flashes, an oxidizer (an oxidizing agent) and a fuel (a

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 2/10

reducing agent) are used. A common mixture involves potassium perchlorate as the oxidizer and aluminum and sulfur as the fuel. The perchlorate

oxidizes the fuel in a very exothermic reaction, which produces a brilliant flash, due to the aluminum, and a loud report from the rapidly expanding gases produced. For a color effect, an element with a colored emission spectrum is included. Recall that the electrons in atoms can be raised to higher-energy orbitals when the atoms absorb energy. The excited atoms can then release this excess energy by emitting light of specific wavelengths, often in the visible region. In fireworks, the energy to excite the electrons comes from the reaction between the oxidizer and fuel.

A typical aerial shell used in fireworks displays. Time-delayed fuses cause a shell to explode in stages. In this case a red starburst occurs first, followed by a blue starburst, and finally a flash and loud report.

Yellow colors in fireworks are due to the -nm emission of sodium ions. Red colors come from strontium salts emitting at nm and from to nm. This red color is familiar from highway safety flares. Barium salts give a green color in fireworks, due to a series of emission lines between and nm. A really good blue color, however, is hard to obtain. Copper salts give a blue color, emitting in the

- to -nm region. But difficulties occur because the oxidizing agent, potassium chlorate , reacts with copper salts to form copper chlorate, a highly explosive compound that is dangerous to store. (The use of in fireworks has been largely abandoned because of its explosive hazards.) Paris green, a copper salt containing arsenic, was once used extensively but is now considered to be too toxic.

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 3/10

In recent years the colors produced by fireworks have become more intense because of the formation of metal chlorides during the burning process. These gaseous metal chloride molecules produce colors much more brilliant than do the metal atoms by themselves. For example, strontium chloride produces a much brighter red than do strontium atoms. Thus, chlorine-donating compounds are now included in many fireworks shells.

A typical aerial shell is shown in the diagram. The shell is launched from a mortar (a steel cylinder) using black powder as the propellant. Time-delayed fuses are used to fire the shell in stages. A list of chemicals commonly used in fireworks is given in the table.

Although you might think that the chemistry of fireworks is simple, the achievement of the vivid white flashes and the brilliant colors requires complex combinations of chemicals. For example, because the white flashes produce high flame temperatures, the colors tend to wash out. Thus oxidizers such as are commonly used with fuels that produce relatively low flame temperatures. An added difficulty, however, is that perchlorates are very sensitive to accidental ignition and are therefore quite hazardous. Another problem arises from the use of sodium salts. Because sodium produces an extremely bright yellow emission, sodium salts cannot be used when other colors are desired. Carbon-based fuels also give a yellow flame that masks other colors, and this limits the use of organic compounds as fuels. You can see that the manufacture of fireworks that produce the desired effects and are also safe to handle requires careful selection of chemicals. And, of course, there is still the dream of a deep blue flame.

Fireworks in Washington, D.C.

javascript://

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 4/10

PhotoDisc/Getty Images

Chemicals Commonly Used in the Manufacture of Fireworks

Oxidizers Fuels Special Effects

Potassium nitrate Aluminum Red flame: strontium nitrate, strontium carbonate

Potassium chlorate

Magnesium Green flame: barium nitrate, barium chlorate

Potassium perchlorate

Titanium Blue flame: copper carbonate, copper sulfate, copper oxide

Ammonium perchlorate

Charcoal Yellow flame: sodium oxalate, cryolite

Barium nitrate Sulfur White flame: magnesium, aluminum

Barium chlorate Antimony sulfide Gold sparks: iron filings, charcoal

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 5/10

Oxidizers Fuels Special Effects

Strontium nitrate Dextrin White sparks: aluminum, magnesium, aluminum–magnesium alloy, titanium

Red gum Whistle effect: potassium benzoate or sodium salicylate

Polyvinyl chloride White smoke: mixture of potassium nitrate and sulfur

Colored smoke: mixture of potassium chlorate, sulfur, and organic dye

These observations can be explained by assuming that electromagnetic radiation is quantized (consists of photons), and that the threshold frequency represents the minimum energy required to remove the electron from the metal’s surface.

Because a photon with energy less than cannot remove an electron, light with a frequency less than the threshold frequency produces no electrons (Fig. 7.4). On the other hand, for light where , the energy in excess of that required to remove the electron is given to the electron as kinetic energy (KE):

Because in this picture the intensity of light is a measure of the number of photons present in a given part of the beam, a greater intensity means that more photons are available to release electrons (as long as for the radiation).

Figure 7.4

The photoelectric effect. (a) Light with frequency less than the threshold frequency produces no electrons. (b) Light with frequency higher than the threshold frequency causes electrons to be emitted from the metal.

javascript://

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 6/10

In a related development, Einstein derived the famous equation

in his special theory of relativity published in 1905. The main significance of this equation is that energy has mass. This is more apparent if we rearrange the equation in the following form:

Using this form of the equation, we can calculate the mass associated with a given quantity of energy. For example, we can calculate the apparent mass of a photon. For electromagnetic radiation of wavelength , the energy of each photon is given by the expression

Then the apparent mass of a photon of light with wavelength is given by

The photon behaves as if it has mass under certain circumstances. In 1922 American physicist Arthur Compton (1892–1962) performed experiments involving collisions of X rays and electrons that showed that photons do exhibit the apparent mass calculated from the preceding equation. However, it is clear that photons do not have mass in the classical sense. A photon has mass only in a relativistic sense—it has no rest mass.

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 7/10

We can summarize the important conclusions from the work of Planck and Einstein as follows:

Energy is quantized. It can occur only in discrete units called quanta.

Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well. This phenomenon is sometimes referred to as the dual nature of light (the statement that light exhibits both wave and particulate properties.) (Fig. 7.5).

Figure 7.5

Electromagnetic radiation exhibits wave properties and particulate properties. The energy of each photon of the radiation is related to the wavelength and frequency by the equation .

Thus light, which previously was thought to be purely wavelike, was found to have certain characteristics of particulate matter. But is the opposite also true? That is, does matter that is normally assumed to be particulate exhibit wave properties? This question was raised in 1923 by a young French physicist named Louis de Broglie (1892–1987). To see how de Broglie supplied the answer to this question, recall that the relationship between mass and wavelength for electromagnetic radiation is . For a particle with velocity , the corresponding expression is

Rearranging to solve for , we have

This equation, called de Broglie’s equation, allows us to calculate the wavelength for a particle, as shown in Example 7.3.

Interactive Example 7.3

Calculations of Wavelength

javascript://

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 8/10

Compare the wavelength for an electron ( kg) traveling at a speed of m/s with that for a ball ( kg) traveling at m/s.

Solution

We use the equation , where

since

For the electron,

For the ball,

See Exercises 7.59, 7.60, 7.61 and 7.62

Notice from Example 7.3 that the wavelength associated with the ball is incredibly short. On the other hand, the wavelength of the electron, although still quite small, happens to be on the same order as the spacing between the atoms in a typical crystal. This is important because, as we will see presently, it provides a means for testing de Broglie’s equation.

Diffraction (the scattering of light from a regular array of points or lines, producing constructive and destructive interference.) results when light is scattered from a regular array of points or lines. You may have noticed the diffraction of light from the ridges and grooves of a compact disc. The colors result because the various wavelengths of visible light are not all scattered in the same way. The colors are “separated,” giving the same effect as light passing through a prism. Just as a regular arrangement of ridges and grooves produces diffraction, so does a regular array of atoms or ions in a crystal, as shown in Figure 7.6. For example, when X rays are directed onto a crystal of a particular nickel/titanium alloy, the scattered radiation produces a diffraction pattern of bright spots and dark areas on a photographic plate (Fig. 7.6). This occurs because the scattered light can interfere constructively (the peaks and troughs of the beams are in phase) to produce a

javascript://

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 9/10

bright area [Fig. 7.6(a)] or destructively (the peaks and troughs are out of phase) to produce a dark spot [Fig. 7.6(b)].

Figure 7.6

A diffraction pattern of a beryl crystal. (a) A light area results from constructive interference of the waves. (b) A dark area arises from destructive interference of the waves.

Dr. David Wexler/Science Source

A diffraction pattern can be explained only in terms of waves. Thus, this phenomenon provides a test for the postulate that particles such as electrons have wavelengths. As we saw in Example 7.3, an electron with a velocity of m/s (easily achieved by acceleration of the electron in an electric field) has a wavelength of about m, which is roughly the distance between the ions in a crystal such as sodium chloride. This is important because diffraction occurs most efficiently when the spacing between the scattering points is about the same as the wavelength of the wave being diffracted. Thus, if electrons really do have an associated wavelength, a crystal should diffract electrons. An experiment to test this idea was carried out in 1927 by C. J. Davisson and L. H. Germer at Bell Laboratories. When they directed a beam of electrons at a nickel crystal, they observed a diffraction pattern similar to that seen from the diffraction of X rays. This result verified de Broglie’s relationship, at least for electrons. Larger chunks of matter, such as balls, have such small wavelengths (see Example 7.3) that they are impossible to verify experimentally. However, we believe that all matter obeys de Broglie’s equation.

Now we have come full circle. Electromagnetic radiation, which at the turn of the twentieth century was thought to be a pure waveform, was found to possess particulate properties.

javascript://

11/25/2018 Print Preview

https://ng.cengage.com/static/nb/ui/evo/index.html?eISBN=9781305957534&id=173840462&nbId=491048&snapshotId=491048&dockAppUid=101& 10/10

Conversely, electrons, which were thought to be particles, were found to have a wavelength associated with them. The significance of these results is that matter and energy are not distinct. Energy is really a form of matter, and all matter shows the same types of properties. That is, all matter exhibits both particulate and wave properties. Large pieces of matter, such as baseballs, exhibit predominantly particulate properties. The associated wavelength is so small that it is not observed. Very small “bits of matter,” such as photons, while showing some particulate properties, exhibit predominantly wave properties. Pieces of matter with intermediate mass, such as electrons, show clearly both the particulate and wave properties of matter.

© 2018 Cengage Learning Inc. All rights reserved. No part of this work may by reproduced or used in any form or by any means - graphic, electronic, or mechanical, or in any other manner - without the written permission of the copyright holder.