Answer 4_6_7
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When
cadmium light is viewed through a diffraction grating having 500 lines per
millimetre, the following spectral lines were observed at the stated
angles.
Angle
(o)
Colour
18.78
red
14.74
green
13.89
light blue
13.53
dark blue Find
the wavelength of these lines.
Find the other angles at which spectral lines would be observed.
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Work out the spacing: d = 0.001 m = 2.00 ´
10-6 m (P)
500 m-1 |
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Formula: l
= d sin q n |
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For all of these angles, n = 1, so we can ignore it (P). |
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For red light,
l = 2.00 ´ 10-6
´ sin 18.78o
= 6.44 ´ 10-7 m = 644 nm (P) |
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We can do similar calculations to find the wavelengths
of all the other spectral lines:
green - 509 nm; light blue - 480 nm;
dark blue - 468 nm. (P) |
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To work out the second order angles we need to use:
sin q
= nl
d |
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For red light:
sin q =
2 ´
6.44 ´
10-7 m
= 0.644 (P)
2.00 × 10-6 m |
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Þ q = sin -1
0.644 = 40.09o (not
equal to 2 × 18.78o)
(P) |