X-rays of wavelength 0.0620 nm are scattered from a crystal with a grazing angle of 11.1°. Assume m = 1 for this process. Calculate the spacing between the crystal planes. d = nm

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Chapter1: Units, Trigonometry. And Vectors
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ml (0.0700 nm)
2d 2(0.314 nm)
Find the grazing angle corresponding
sin e =
0.111
to m = 1, for first-order interference:
e = sin-1(0.111) = 6.37°
Repeat the calculation for third-order
interference (m = 3):
mì 3(0.0700 nm)
sin e =
2d
= 0.334
2(0.314 nm)
e = sin(0.334) = 19.5°
LEARN MORE
REMARKS Notice there is little difference between this kind of problem and a Young's slit experiment.
QUESTION If the grazing angle is smaller, the distance between planes in the crystal lattice is:
larger.
O the same.
O smaller.
PRACTICE IT
Use the worked example above to help you solve this problem. If the spacing between certain planes in a
crystal of calcite (CaCO,) is 0.313 nm, find the grazing angles at which first- and third-order interference
will occur for x-rays of wavelength 0.0661 nm.
0, = 6.06
82 =| 18.47
EXERCISE
HINTS: GETTING STARTED |
I'M STUCK!
X-rays of wavelength 0.0620 nm are scattered from a crystal with a grazing angle of 11.1°. Assume m = 1
for this process. Calculate the spacing between the crystal planes.
d =
nm
Transcribed Image Text:ml (0.0700 nm) 2d 2(0.314 nm) Find the grazing angle corresponding sin e = 0.111 to m = 1, for first-order interference: e = sin-1(0.111) = 6.37° Repeat the calculation for third-order interference (m = 3): mì 3(0.0700 nm) sin e = 2d = 0.334 2(0.314 nm) e = sin(0.334) = 19.5° LEARN MORE REMARKS Notice there is little difference between this kind of problem and a Young's slit experiment. QUESTION If the grazing angle is smaller, the distance between planes in the crystal lattice is: larger. O the same. O smaller. PRACTICE IT Use the worked example above to help you solve this problem. If the spacing between certain planes in a crystal of calcite (CaCO,) is 0.313 nm, find the grazing angles at which first- and third-order interference will occur for x-rays of wavelength 0.0661 nm. 0, = 6.06 82 =| 18.47 EXERCISE HINTS: GETTING STARTED | I'M STUCK! X-rays of wavelength 0.0620 nm are scattered from a crystal with a grazing angle of 11.1°. Assume m = 1 for this process. Calculate the spacing between the crystal planes. d = nm
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