PSCI 1414 GENERAL ASTRONOMY THE NATURE OF LIGHT PART 2: BLACKBODY RADIATION AND SPECTRAL ANALYSIS ALEXANDER C. SPAHN

BLACKBODY RADIATION The figure depicts quantitatively how the radiation from a dense object depends on its Kelvin temperature. Each curve in this figure shows the intensity of light emitted at each wavelength by a dense object at a given temperature: 3000 K (the temperature of a “cool” star), 6000 K (around the temperature of our Sun), and 12,000 K (the temperature of a “hot” star). In other words, the curves show the spectrum of light emitted by such an object.

BLACKBODY RADIATION The figure shows that the higher the temperature, the greater the intensity of light at all wavelengths. One way to understand this response to temperature is that the emitted light results from the motion of the material’s atoms and molecules, which, as we saw, increases with temperature

BLACKBODY RADIATION The temperature not only indicates the total intensity of the light, but also the shape of its spectrum. The most important feature in the spectrum—the dominant wavelength—is called the wavelength of maximum emission, at which the curve has its peak and the intensity of emitted energy is strongest. The location of the peak also changes with temperature: The higher the temperature, the shorter the wavelength of maximum emission.

BLACKBODY RADIATION To summarize these observations: The higher an object’s temperature, the more intensely the object emits electromagnetic radiation and the shorter the wavelength at which it emits most strongly. We will make frequent use of this general rule to analyze the temperatures of celestial objects such as planets and stars.

BLACKBODY RADIATION The curves in the figure are drawn for an idealized type of dense object called a blackbody. A perfect blackbody does not reflect any light at all; instead, it absorbs all radiation falling on it. Because it reflects no electromagnetic radiation, the radiation that it does emit is entirely the result of its temperature.

BLACKBODY RADIATION Ordinary objects, like tables, textbooks, and people, are not perfect blackbodies; they reflect light, which is why they are visible. A star such as the Sun, however, behaves very much like a perfect blackbody, because it absorbs almost completely any radiation falling on it from outside. The light emitted by a blackbody is called blackbody radiation, and the curves are often called blackbody curves.

TEMPERATURE AND THERMAL ENERGY This figure shows the blackbody curve for a temperature of 5800 K as well as the intensity curve for light from the Sun. The peak of both curves is at a wavelength of about 500 nm, near the middle of the visible spectrum. Note how closely the observed intensity curve for the Sun matches the blackbody curve. This is a strong indication that the temperature of the Sun’s glowing surface is about 5800 K—a temperature that we can measure across a distance of 150 million kilometers!

TEMPERATURE AND THERMAL ENERGY Blackbody radiation depends only on the temperature of the object emitting the radiation, not on the chemical composition of the object. The light emitted by molten gold at 2000 K is very nearly the same as that emitted by molten lead at 2000 K. The intensity curve for the Sun (a typical star) is not precisely that of a blackbody. We will see that the differences between a star’s spectrum and that of a blackbody allow us to determine the chemical composition of the star.

WIEN’S LAW

CALCULATION CHECK 5-2 Which wavelength of light would our Sun emit most if its temperature were twice its current temperature of 5800 K? Wien’s law can be rearranged to calculate the temperature of a star as T = K m ÷ (5800 K × 2) = 2.5x10 -7 m = 250 nm, which is ultraviolet.

STEFAN-BOLTZMANN LAW The other useful formula for the radiation from a blackbody involves the total amount of energy the blackbody radiates at all wavelengths. Energy is usually measured in joules (J), named after the nineteenth-century English physicist James Joule. The joule is a convenient unit of energy because it is closely related to the familiar watt (W): 1 watt is 1 joule per second, or 1 W = 1 J/s = 1 J s −1. For example, a 100-watt lightbulb uses energy at a rate of 100 joules per second, or 100 J/s.

STEFAN-BOLTZMANN LAW The amount of energy emitted by a blackbody depends both on its temperature and on its surface area. These characteristics make sense: A large burning log radiates much more heat than a burning match, even though the temperatures are the same. To consider the effects of temperature alone, it is convenient to look at the amount of energy emitted from each square meter of an object’s surface in a second. This quantity is called the energy flux(F).

STEFAN-BOLTZMANN LAW Flux means “rate of flow,” and thus F is a measure of how rapidly energy is flowing out of the object. It is measured in joules per square meter per second, usually written as J/m 2 /s or J m −2 s −1. Alternatively, because 1 watt equals 1 joule per second, we can express flux in watts per square meter (W/m 2, or W m −2 ).

STEFAN-BOLTZMANN LAW

CONCEPT CHECK 5-8 Is it ever possible for a cooler object to emit more energy than a warmer object? Yes. If the cooler object is much larger than the warmer object, the cooler object can emit a greater total energy. The energy flux F refers to the energy emitted per second for each square meter of surface area, so even for a cool object, the larger the object, the more energy it radiates. This is why some stars (called red giants) that are much larger than our Sun are actually brighter than our Sun, even though they are cooler.

PHOTONS In 1905, the great physicist Albert Einstein developed a radically new model for the nature of light. Central to this new picture is that light is made out of particles! Each particle of light is called a photon, which is a distinct packet of electromagnetic energy. Photons have a dual nature in that they are both particle-like and wavelike.

PHOTONS They are particle-like in the sense that they are the small packets of energy that make up light. As expected with particles, you can count the number of photons in an electromagnetic wave. But, photons are also wave-like because each one is itself a wave, where each photon has the same wavelength as the electromagnetic wave of which it is a small part. As expected with waves, photons exhibit interference patterns when passed through a double- slit experiment

PHOTONS The energy of each photon is related to the wavelength of light: the longer the wavelength, the lower the energy. Thus, a photon of red light (wavelength λ = 700 nm) has less energy than a photon of violet light (λ = 400 nm). Conversely, the shorter a photon’s wavelength, the higher its energy.

PHOTONS

SPECTRAL ANALYSIS In 1814 the German master optician Joseph von Fraunhofer repeated the classic experiment of shining a beam of sunlight through a prism. But this time Fraunhofer subjected the resulting rainbow-colored spectrum to intense magnification. To his surprise, he discovered that the solar spectrum contains hundreds of fine, dark lines, now called spectral lines.

SPECTRAL ANALYSIS spectral line: In a light spectrum, an absorption or emission feature that is at a particular wavelength. Dark spectral line arises when light at a specific wavelength is at least partially absorbed so that the spectrum appears darker; it is also called an absorption line. Fraunhofer counted more than 600 dark lines in the Sun’s spectrum; today we know of more than 30,000.

SPECTRAL ANALYSIS Half a century later, chemists discovered that they could produce spectral lines in the laboratory and use these spectral lines to analyze what kinds of atoms different substances are made of. Chemists had long known that many substances emit distinctive colors when sprinkled into a flame. To facilitate study of these colors, around 1857 the German chemist Robert Bunsen invented a gas burner (today called a Bunsen burner) that produces a clean flame with no color of its own.

SPECTRAL ANALYSIS Bunsen’s colleague, the Prussian-born physicist Gustav Kirchhoff, suggested that the colored light produced when substances were added to the flame might best be studied by passing the resulting light through a prism. The two scientists promptly discovered that the spectrum from the flame consists of a pattern of thin, bright spectral lines against a dark background. A bright spectral line arises because at least some additional light is being emitted at a specific wavelength; it is also called an emission line.

SPECTRAL ANALYSIS Kirchhoff and Bunsen then found that each chemical element produces its own unique pattern of spectral lines. Thus was born in 1859 the technique of spectral analysis: the identification of atoms and molecules by their unique patterns of spectral lines. You can easily see that each substance produces a unique pattern of spectral lines; each pattern can be thought of as a spectral “fingerprint” for identification. This is enormously important in astronomy because it allows us to determine the detailed composition of distant planets and stars.

THE SOLAR SYSTEM There is a direct connection between these two types of spectra. These connections are summarized in three statements about spectra that are known as Kirchhoff’s laws. A hot opaque body, such as a perfect blackbody, or a hot, dense gas produces a continuous spectrum—a complete rainbow of colors without any spectral lines. Note: a blackbody is an idealized type of dense object that does not reflect any light at all; instead, it absorbs all radiation falling on it.

THE SOLAR SYSTEM A hot, transparent gas produces an emission line spectrum—a series of bright spectral lines against a dark background.

THE SOLAR SYSTEM A cool, transparent gas in front of a source of a continuous spectrum produces an absorption line spectrum—a series of dark spectral lines among the colors of the continuous spectrum.

FOR NEXT TIME… Read Chapter 16 of the text Homework 14: Will be posted later today online, due Monday (no class Friday)