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Diffraction grating

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1) If a diffraction grating has 6,000 grooves per centimeter, to what angle will the first order constructive interference "line" of the Hydrogen Alpha (red) emission be diffracted?

2) Atoms of the hydrogen gas enveloping a particular star absorb the Hydrogen Alpha wavelength from the white light emanating from the surface of the star and reemit that color in random directions, causing the spectrum received by observers on Earth to have a dark line due to the missing light. (Discovered by Joseph Fraunhoffer) Suppose the measured wavelength of the dark line is found to be 6555 Angstroms. Is the radial motion of the star toward or away from Earth? Compute how fast the star is moving relative to the earth.

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Solution Preview

1) For single-line sources, the constructive interference fringes of a diffraction grating are given by d*sin(theta) = m(lambda)

d is the distance between pairs of grooves. Here, we have 6000 grooves per centimeter, or 5999 spaces between grooves, giving

d = 1/5999 cm

Lambda is the wavelength of ...

Solution Summary

Diffraction grating is featured. The interference line of the hydrogen alpha is examined for emission diffracted.

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Diffraction of Light: Diffraction Grating

1. A diffraction grating with 2.10E3 slits per centimeter is used to measure the wavelengths emitted by hydrogen gas.
At what angles in the first-order spectrum would you expect to find the two violet lines of wavelengths 434 nm
and 410 nm?
(a) At what angle in the first-order spectrum would you expect to find the first violet line of wavelengths
434 nm?
(b) At what angle in the first-order spectrum would you expect to find the second violet line of
wavelength 410 nm?

2. What is the longest wavelength that can be observed in the fifth-order (m=5) spectrum using a diffraction grating with
3.60E3 slits per centimeter? (Unit: nm)
All answers must have three significant digits unless otherwise specified.

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