Figure 1 shows a type of apparatus for investigating the speed distribution f (v

Question

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 contains aluminium at T = 900 °C, which emerges as a monatomic beam. Calculate the speed vmp and the corresponding rotation speed at which the largest rate of arrival for aluminium atoms is observed. (The molar mass of aluminium is 0.0270 kg mol1.)

Explanation / Answer

we have that K=3kT/2 where K be kinetic energy of the atom v=sqrt(3RT/M)= 1040(m/s). -- after a period of time T. we have T*w=alpha=30 deg. T*1040=L=262e-3 so w=30/T=30/(262e-3/1040)=1.19e5(deg/s). =4156(rad/s)

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