An experiment to investigate the velocity distribution of gas atoms uses a molecular velocity selector consisting of two parallel circular disks mounted coaxially on a common shaft in a vacuum chamber. The distance between the two disks is exactly 0.500 m0.500\text{ m}0.500 m.
A radial slot in the first disk allows a pulse of gas to pass. A corresponding detector slot in the second disk is angularly offset by 30.0∘30.0^\circ30.0∘ relative to the first slot.
Show that the speed of a gas atom that passes through the first slot and successfully exits through the detector slot on the second disk is exactly 1500 m s−11500\text{ m s}^{-1}1500 m s−1, given that:
The speed calculated in part (a) is equal to crmsc_{\text{rms}}crms, the root mean square speed of the Helium atoms in the gas source. The molar mass of Helium is 0.00400 kg mol−10.00400\text{ kg mol}^{-1}0.00400 kg mol−1. Calculate the temperature of the gas source. (Use molar gas constant R=8.31 J mol−1 K−1R = 8.31\text{ J mol}^{-1}\text{ K}^{-1}R=8.31 J mol−1 K−1)
The initial pressure of the Helium gas at this constant temperature inside the source chamber of volume 8.00×10−3 m38.00 \times 10^{-3}\text{ m}^38.00×10−3 m3 is 1.50×105 Pa1.50 \times 10^5\text{ Pa}1.50×105 Pa. During the run, the pressure drops to 1.35×105 Pa1.35 \times 10^5\text{ Pa}1.35×105 Pa as atoms escape. Calculate, in moles, the quantity of Helium gas that has exited the chamber. (Use the temperature value calculated in part (b).)
