# hw6 - common element in the Sun 2 Assume a 1-dimensional...

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Homework Problem Set No. 6 – Physics 17 Due in class, Wednesday, November 12 1. The escape velocities from the surface of the Earth and the Moon are 11.1 km s - 1 and 2.4 km s - 1 , respectively. Assume a temperature of 300 K on each object. [They are both warmed by the Sun so this is not too bad for a ﬁrst approximation.] What is the probability that an oxygen atom at 300 K has a speed comparable to the escape velocity from the surface of the Earth and from the surface of the Moon? If a molecule collides every 10 - 4 s and if the Solar System has a lifetime of 4.5 × 10 9 yr, make a rough esti- mate of the fraction of their initial atmospheres that the Earth and the Moon might have lost. Now consider a hydrogen atom on the surface of the Earth. Can you explain why the Earth’s atmosphere has oxygen but no hydrogen even though hydrogen is the most
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Unformatted text preview: common element in the Sun? 2. Assume a 1-dimensional system where the energy, E, varies as E = E n 4 where n is the quantum number. At temperature, T , what is the mean energy of the system? 3. Consider a two level system with energy spacing E . Find the mean energy of the system as a function of temperature, T . What happens in the limits of high T and low T ? 4. Consider the Maxwell-Boltzmann distribution. Compute the mean values of v x and v 2 x for a gas whose atoms have mass m . 5. Consider the Maxwell-Boltzmann distribution for a gas with atoms of mass m and temperature T . Let n denote the number density of molecules. What is the mean rate (collisions m-2 s-1 at which the atoms collide with a ﬂat wall? 1...
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