The principle of wave-particle duality tells us that a particle with momentum p (= mv) has...

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The principle of wave-particle duality tells us that a particle with momentum p (= mv) has an associated de Broglie wavelength of λ =h/p; this wavelength increases as λx a as the universe expands. The total energy density of a gas of particles can be written as & nE, where 'n' is the number density of particles, and 'E' is the energy per particle. For simplicity, let's assume that all the gas particles have the same mass 'm' and momentum 'p'. The energy per particle is then simply E = (m²c² + (h²c²/A²))¹/2 Compute the equation-of-state parameter 'w' for this gas as a function of the scale factor a. Show that W= 1 aa-2 31+xza-² -2 where to po/mc is a dimensionless momentum. The principle of wave-particle duality tells us that a particle with momentum p (= mv) has an associated de Broglie wavelength of λ =h/p; this wavelength increases as λx a as the universe expands. The total energy density of a gas of particles can be written as & nE, where 'n' is the number density of particles, and 'E' is the energy per particle. For simplicity, let's assume that all the gas particles have the same mass 'm' and momentum 'p'. The energy per particle is then simply E = (m²c² + (h²c²/A²))¹/2 Compute the equation-of-state parameter 'w' for this gas as a function of the scale factor a. Show that W= 1 aa-2 31+xza-² -2 where to po/mc is a dimensionless momentum.