help A coherent beam of white light shines through a diffraction grating (7000 s

Question

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A coherent beam of white light shines through a diffraction grating (7000 slits per cm.) Choose a wavelength from the red portion of the visible spectrum. Determine the angular position of the first-order (m=1) bright line for this wavelength. Repeat part a) for a wavelength in the green portion of the spectrum. The element Technetium (element 43) has no stable isotopes. The only naturally occurring Technetium on Earth comes from Uranium fission, so finding some Technetium may be evidence of nuclear weapons activity. Technetium produces a spectrum that includes a line at 485.4 nm. At what angle will this line appear in our grating?

Explanation / Answer

a)slit seperation = 10^-2/7000 = 1.428*10^-6 m

Taking wavelength of 650 nm,

then d sin theta = m*wavelength

1.428*10^-6*sin theta = 650*10^-9

then theta = 27.06 degrees.

b)Taking wavelength of 510nm,

then d sin theta = m*wavelength

1.428*10^-6*sin theta = 510*10^-9

then theta = 20.925 degrees.

c)for wavelength = 485.4 nm

then d sin theta = m*wavelength

1.428*10^-6*sin theta = 485.4 *10^-9

then theta = 19.872 degrees.

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