Concept explainers
(a)
The angular dispersion of the grating is
(a)
Answer to Problem 73AP
The angular dispersion of the grating is
Explanation of Solution
Formula to calculate the angles of bright beams diffracted from the grafting is,
Here,
Differentiate equation (I) with respect to
Conclusion:
Therefore, the angular dispersion of the grating is
(b)
The angular separation of the two wavelengths in the second order spectrum.
(b)
Answer to Problem 73AP
The angular separation of the two wavelengths in the second order spectrum is
Explanation of Solution
Number of equally spaced slit to analyze the spectrum of mercury is 8,000. The square grating on each side is
The wavelengths of the incident lights are
Write the expression of the average wavelength.
Formula to calculate the spacing between the adjacent slit is,
Substitute 0.02 for square grating and 8000 for number of equally spaced slits in equation (II).
Substitute
Formula to calculate the separation angle between the lines is,
Here,
The difference in wavelength of lights is,
Substitute 2 for
Conclusion:
Therefore, the angular separation of the two wavelengths in the second order spectrum is
Want to see more full solutions like this?
Chapter 38 Solutions
Physics for Scientists and Engineers with Modern Physics, Technology Update
- The 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_forwardAn 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_forward
- A metal with body centered cubic (bcc) structure show the first (i.e. smallest angle) diffraction peak at a Bragg angle of 0 = 30°. The wavelength of X-ray used is 2.1 Å. The volume of the PRIMITIVE unit cell of the metal is (a) 26.2 (Å)³ (b) 13.1(Á)³ (c) 9.3 (Á)³ (d) 4.6 (Ấ)³arrow_forwardMonochromatic X-rays are incident on a crystal. The first-order Bragg peak is observed when the angle of incidence is 34.0°. The crystal spacing is known to be 0.347 nm. What is the wavelength of the X rays?arrow_forwardHow many modes can exist in a spherical cavity of diameter 4.0 cm if illuminated by light with a central wavelength of 500 nm with a spectral spread of 0.10 nm?arrow_forward
- When a diffraction pattern of a crystalline solid is recorded using an X-ray beam of wavelength 0.26 nm, the first order diffraction peak occurs at a scattering angle of 35°. If the error in the measurements of angle and wayelength are 1° and 0.01 nm respectively, then determine the error in measuring the interplanar spacing. (a) 22.86 nm (b) 32.38 nm (c) 15.2 nm (d) 13.2 nmarrow_forwardIn the figure, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.820 nm makes an angle θ = 62.3˚ with the top face of the crystal. What is the unit cell size a0?arrow_forwardWhite light is incident normally on a diffraction grating with 300 lines/mm. The resulting diffracted light is then focused via a lens of focal length ƒ = +75 mm onto a detector. The lens and detector are aligned so that the first-order diffracted light at 550 nm is co-axial with the lens and focuses onto the centre of the detector. The hydrogen atom can emit two spectral lines (called Ha, Hẞ) at respective wavelengths 656 nm and 486 nm. Calculate the separation on the detector between the first-order diffracted light of these latter two wavelengths.arrow_forward
- First-order Bragg scattering from a certain crystal occurs at an angle of incidence of 63.8°; see figure below. The wavelength of the x-rays is 0.261nm. Assuming that the scattering is from the dashed planes shown, find the unit cell size ao. 63.8° X raysarrow_forwardFor red light of λ = 660 nm , what are f, ω , and k?arrow_forwardAn 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 of 24.2o,25.7o,29.1o,and 41.0o when projected on a diffraction grating having 10,000 lines per centimeter?arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning