Laser cooling is used to cool dilute vapours of sodium atoms to 2mK. Passing the

Question

Laser cooling is used to cool dilute vapours of sodium atoms to 2mK. Passing them through multiple apertures forms an atomic beam, that is injected into the atom interferometer shown on the right. The standing light waves are created with a laser at Lambda = 532nm. What is the rms speed v_rms of a Sodium atom (Lambda=23) in a gas at 2.0mK? The laser beam acts as a grating. Calculate the first order diffraction angle of the sodium atoms travelling with the rms speed from question (a). How far are points B and C if the second standing wave is 20cm after the first? Because Interference is observed between the two paths, each atom is apparently present at both points B and C. Describe in your own words what this experiment tells you about the nature of matter.

Explanation / Answer

a) Rms speed =   sqrt(3RT/M)

                          = sqrt(3 * 8.314 * 0.002/0.023)

                         = 1.472 m/sec

b)    Here, d * sin(theta) = n * lambda

=>     sin(theta) =   1 * 532 * 10-9/(0.01472 * 10-3)

=> diffraction angle = 2.071 degree

c) Far apart are points B and C =    sin2.071 * 20

                                                  = 0.722 cm

Part B)   It tells about the wave nature of matter. It tells that the matter has the low molecular mass .

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