Problems on Crystallography and Ultrasonic wave
1. In a Bragg’s spectrometer using set of atomic planes of a crystal of interplanner spacing 2.8 Å,the glancing angle for the first order maximum was
10◦ . Find the wavelength of X-rays employed. At what angle would the
second order maxima occur ?
2. Calculate the glancing angle of the (110) plane of a simple cubic crystal
(a=2.814Å) corresponding to second-order diffraction maxima for the Xrays wavelength 0.710 Å.
3. Electrons are accelerated to 344 volts and are reflected from a crystal. The
first reflection maxima occurs when the glancing angle is 60 ◦ . Determine
the inter planner spacing of crystal.
4. Deduce the Miller indices of a plane which cuts off intercepts in the ratio
1a : 3b : −2c along the three axes, where a, b, c are primitives.
5. Deduce the Miller indices of a plane which cuts off intercepts in the ratio
3a : −2b : 3c
2 along the three axes, where a, b, c are primitives.
6. The lattice constant for a cubic lattice is a. Deduce the spacing between
(011), (101), (112) planes.
7. Find the ratio of intercepts on the three axes by (1, 3, 2) planes in a simple
cubic lattice.
8. In a tetragonal lattice a = b = 2.5Å,c = 1.8Å. Deduce the lattice spacing
between (111) planes.
9. Find the frequency to which a piezoelectric oscillator circuit should be
turned so that a piezoelectric crystal of 0.1 cm thickness vibrates in its
fundamental mode to generate ultrasonic waves. Young’s modulus and
density of material of the crystal are 8 × 1010 N m–2 and 2.654 × 103
kgm–3 respectively.
10. Calculate the natural frequency of 30 mm of iron rod. The density of
iron rod and Young’s modulus are 7.25 × 103 kg/m3 and 115 × 109 N/m2
respectively. Can you use it in magnetostriction oscillator to produce
ultrasonic waves?
11. Calculate the capacitance to produce ultrasonic waves of 106 Hz with an
inductance of 1 Henry.
12. A quartz crystal of thickness 1 mm is vibrating at resonance. Calculate the
fundamental frequency for first overtone. Given Y for quartz is 7.9 × 1010
N m−2 and ρ for quartz is 2650kgm−3 .
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13. In a submarine equiped with sonar, the time delay between the generation
of a pulse and its echo after reflection from an enemy submarine is observed
to be 80 s. If the speed of sound in water is 1460 m/s . What is the
distance of enemy submarine.
14. Considering quality factor of sonometer wire of frequency 260 Hz as 2000,
calculate the relaxation time.
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