12. A 368 g sample of water absorbs infrared radiation at 1.06 × 104 nm from a carbon dioxide laser. Suppose all the absorbed radiation is converted to heat. Calculate the number of photons at this wavelength required to raise the temperature of the water by 5.00ºC.

(a) Which color in the visible spectrum has the highest frequency? Which has the lowest frequency? (b) Is the wavelength of the radiation used in a microwave oven (2.45 GHz) longer or shorter than that from your favorite FM radio station (for example, 91.7 MHz)? (c) Are the wavelengths of x-rays longer or shorter than those of ultraviolet light? (d) Calculate the frequency of green light with a wavelength of 510. nm.

RGB color television and computer displays use cathode ray tubes that produce colors by mixing red, green, and blue light. If we look at the screen with a magnifying glass, we can see individual dots turn on and off as the colors change. Using a spectrum of visible light, determine the approximate wavelength of each of these colors. What is the frequency and energy of a photon of each of these colors?

An FM radio station found at 103.1 on the FM dial broadcasts at a frequency of 1.031188s1 (103.1 MHz). What is the wavelength of these radio waves in meters?

When a tube containing hydrogen atoms is energized by passing several thousand volts of electricity into the tube, the hydrogen emits light than when passed through a prism, resolves into the "bright line" spectrum shown in Fig. 11.10. Why do hydrogen atoms emit bright lines of specific wavelengths rather than a continuous spectrum?

Answer the following questions about a Blu-ray laser: (a) The laser on a Blu-ray player has a wavelength of 405 nm. In what region of the electromagnetic spectrum is this radiation? What is its frequency? (b) A Blu-ray laser has a power of 5 millwatts (1watt=1Js1). How many photons of light are produced by the laser in 1 hour? (c) The ideal resolution of a player using a laser (such as a Blu-ray player), which determines how close together data can be stored on a compact disk, is determined using the following formula: Resolution =0.60(/NA), where A is the wavelength of the laser and NA is the numerical aperture. Numerical aperture is a measure of the size of the spot of light on the disk; the larger the NA, the smaller the spot. In a typical Blu-ray system, NA = 0.95. If the 405-nm laser is used in a Blu-ray player, what is the closest that information can be stored on a Blu-ray disk? (d) The data density of a Blu-ray disk using a 405-nm laser is 1.5107 bits mm2. Disks have an outside diameter of 120 mm and a hole of 15-mm diameter. How many data bits can be contained on the disk? If a Blu-ray disk can hold 9,400,000 pages of text, how many data bits are needed for a typed page? (Hint: Determine the area of the disk that is available to hold data. The area inside a circle is given by A=r2, where the radius r is one-half of the diameter.)

A baseball weighs 142 g. A professional pitcher throws a fast ball at a speed of 100 mph and a curve ball at 80 mph. What wavelengths are associated with the motions of the baseball? If the uncertainty in the position of the ball is 12 wavelength, which ball (fast ball or curve) has a more precisely known position? Can the uncertainty in the position of a curve ball be used to explain why batters frequently miss it?

Warm objects emit electromagnetic radiation in the infrared region. Heat lamps employ this principle to generate infrared radiation. Water absorbs infrared radiation with wavelengths near 2.80 m. Suppose this radiation is absorbed by the water and converted to heat. A 1.00-L sample of water absorbs infrared radiation, and its temperature increases from 20.0C to 30.0C. How many photons of this radiation are used to heat the water?

Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.

Four types of electromagnetic radiation (EMR) are ultraviolet, microwaves, gamma rays, and visible. All of these types of EMR can be characterized by wavelength, frequency, photon energy, and speed of travel. Define these terms and rank the four types of electromagnetic radiation in order of increasing wavelength, frequency, photon energy, and speed.