The bright yellow sodium line in the sodium spectrum is actually a pair of close

Question

The bright yellow sodium line in the sodium spectrum is actually a pair of closely spaced lines at 589.0 nm and 589.6 nm. You observe the sodium spectrum using a diffraction grating with a spacing of 1800nm .

Part A

Find the angular separation between the two sodium lines in first order.

Express your answer to two significant figures and include the appropriate units.

Part B

Find the angular separation between the two sodium lines in second order.

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Part A)

Apply tan(angle) = m(wavelength)/d

tan(angle) = 1(589 X 10-9)/(1800 X 10-9)

angle = 18.11925 degrees (or 19.10026 degrees if tyour book uses "small angle approximations")

tan(angle) = 1(589.6 X 10-9)/(1800 X 10-9)

angle = 18.13650 degrees (or 19.12047 degrees if tyour book uses "small angle approximations")

Subtract the two and get .0173 degrees (or .202 degrees)

Part B)

tan(angle) = 2(589 X 10-9)/(1800 X 10-9)

angle = 32.20252 degrees (or 40.87754 degrees if tyour book uses "small angle approximations")

tan(angle) = 2(589.6 X 10-9)/(1800 X 10-9)

angle = 33.22925 degrees (or 40.92808 degrees if tyour book uses "small angle approximations")

Subtract the two and get 1.027 degrees (or .0505 degrees)

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