A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, $0.900 \mathrm{~mm} \times 0.300 \mathrm{~mm} \times 10.0 \mathrm{~mm},\( contains \)4 \%$ Xe in a 1: 1 Ne:He mixture at a total pressure of \(66.66 \mathrm{kPa}\). Calculate the number of Xe, Ne, and He atoms in the cell and state the assumptions you need to make in your calculation.

The number of Xe, Ne, and He atoms in the given plasma cell can be calculated using the Ideal Gas Law and partial pressures. First, calculate the volume of the cell: \(V = 2.7 \times 10^{-7} m^3\). Next, find the partial pressures for each gas: \(P_{Xe} = 2.6664 \mathrm{kPa}\), \(P_{Ne} = 32.0008 \mathrm{kPa}\), and \(P_{He} = 32.0008 \mathrm{kPa}\). Then, calculate the number of moles (n) for each gas using the Ideal Gas Law, assuming temperature remains constant throughout the calculation. Finally, use Avogadro's number to convert the number of moles to the number of atoms for each gas. The assumptions made include considering the gases as ideal gases and that the temperature of the gas mixture remains constant.