Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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- An electric current through hydrogen gas produces several distinct wavelengths of visible light. What are the wavelengths of the hydrogen spectrum, if they form first-order maxima at angles 24.2°, 25.7°, 29.1°, and 41.0° when projected on a diffraction grating having 10,000 lines per centimeter?arrow_forwardThe structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which X-ray diffraction can be observed, if X-rays of wavelength 0.085 nm are used?arrow_forwardAs a single crystal is rotated in an x-ray spectrometer (Fig. 3.22a), many parallel planes of atoms besides AA and BB produce strong diffracted beams. Two such planes are shown in Figure P3.38. (a) Determine geometrically the interplanar spacings d1 and d2 in terms of d0. (b) Find the angles (with respect to the surface plane AA) of the n = 1, 2, and 3 intensity maxima from planes with spacing d1. Let = 0.626 and d0 = 4.00 . Note that a given crystal structure (for example, cubic) has interplanar spacings with characteristic ratios, which produce characteristic diffraction patterns. In this way, measurement of the angular position of diffracted x-rays may be used to infer the crystal structure. Figure P3.38 Atomic planes in a cubic lattice.arrow_forward
- The absorption cross section for fluorescein, a dye that is used as a fluorescent probe for biological imaging (see the Chapter Opener image), is 9.25 × 10-16 cm2 molecule-1 at 500 nm. How much light is transmitted through a 1-cm path length by a standard 10-6 M solution of fluoresceinused to label biological samples?arrow_forwardA crystal sample of bacteriorhodopsin, a light-sensitive protein found in halobacteria that responds to light energy, has crystal planes separated by 0.20 nm. If a beam of 12keV x rays illuminates a sample, what angles will give diffraction maxima of the first, second and third order? Express your answers in degrees separated by commas in ascending order.arrow_forwardA third-order diffraction maximum is observed when a 0.862 Å X-ray beam is diffracted by the planes (111) of a copper crystal. The incident and diffracted beams form angles of 38.26° with the planes. Find the distance between adjacent (111) planes.arrow_forward
- A Michelson interferometer is used with red light of wavelength 632.8 nm and is adjusted for a path difference of 20 μm. Determine the angular radius of the (a) first ring observed and (b) the tenth ring observed.arrow_forwardAn X-ray beam of a wavelength 0.15 nm is incident on an NaCl crystal, at 25° to reflecting planes of the crystal. If the first order reflections occurred in the spectrum, find the spacing of the reflecting planes of the crystal. (а) 0.18 pm (b) 0.35 nm (c) 0.18 nm (d) 0.35 pmarrow_forwardA Michelson interferometer is used with red light of wavelength 632.8 nm and is adjusted for a path difference of 20 μm. Determine the angular radius of the a) first (smallest diameter) ring observed and b) the tenth ring observed.arrow_forward
- The limit to the eye’s visual acuity is related to diffraction by the pupil.Randomized VariablesD = 3.05 mmdh = 1.4 m Part (a) What is the angle between two just-resolvable points of light for a 3.05 mm diameter pupil in radians, assuming an average wavelength of 550 nm? Part (b) Take your result to be the practical limit for the eye. What is the greatest possible distance in km a car can be from you if you can resolve its two headlights, given they are 1.4 m apart? Part (c) What is the distance between two just-resolvable points held at an arm’s length (0.800 m) from your eye in mm?arrow_forwardA telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the Moon. If this is done with the Mount Wilson telescope, producing a 2.54 m diameter beam of 613 nm light, what is the minimum angular spread of the beam? Neglecting atmospheric effects, what is the size of the spot this beam would make on the Moon, assuming a lunar distance of 3.84×108 m?arrow_forwardAn astronomer is calibrating a spectrometer that uses a dittraction grating to separate light in order ot increasing wavelength (2,, 1e, and 1). She observes three distinct tirst-order spectral lines at the following respective angles 0, (where m denotes order). 8, = 12.7°, 8, = 14.2°, 0, = 14.9c (a) If the grating has 3,680 qrooves per centimeter, what wavelength (in nm) describes each of these spectral lines? at 8, - 12.70 nm at 6, = 14.2° nm al 8, = 14.9° d = (b) At what angle (in degrees) would each of these lines be found in the second-order spectrum? for 2, 0, - for å, 0, for 2. 8, =arrow_forward
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