Figure 1 Figure 1 shows a type of apparatus for investigating the speed distribu

Question

Figure 1

Figure 1 shows a type of apparatus for investigating the speed distribution f (v) of molecules in a gas. Molecules emerge into a vacuum chamber from an oven held at a constant temperature T, and are collimated by slits into a parallel beam directed towards a pair of discs rotating at a common angular speed , which may be varied. The discs are a fixed distance L apart (L = 262 mm) and contain narrow notches, with the second notch offset from the first by a fixed angle = 30° as shown. If a molecule passes the first notch and is moving at the correct speed v, it will pass through the second notch to be collected at the detector, which records the rate of arrival of molecules.

The oven remains at T = 900 °C, but its contents are changed to silver, also emitted as a monatomic beam. Find the rotation speed at which the largest rate of arrival of silver atoms is observed. (The molar mass of silver is 0.108 kg mol1.)

Explanation / Answer

Let w be omega the angular frequency Theta = 2 pi / 12 = pi/6 w = (pi/6)/t = pi * v / (6 L) since t = L/v 1/2 m v^2 = 3/2 k T is the root mean square speed of the atoms "in" the oven Then v(rms) = (3 k T/m)^1/2 However, it is shown in thermodynamics that the rms speed of the "escaping" speed of the molecules is (4 k T/m)^1/2 m = .108/6.02 * 10E23 to get the mass of the Ag atom Now, substitute to get w the angular frequency

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