6. Use Boltzmann distribution to solve this problem. A system consists of 3,000 particles that can only occupy two energy levels: a nondegen- erate ground state of 0.052 eV and a threefold degenerate excited state at 0.156 eV. If T = 900 K, (a) find the number of particles at each energy level. (b) what is the total energy of the system?

c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable orbits. De Broglie explained what orbits could exist by postulating that electrons (and any- thing else) with momentum p have an associated wavelength λ, given by λ=h/p where h is Planck's constant. i) For an electron orbiting around a proton (the Bohr model), equating the centripetal force with the Coulomb force gives the expression v² = e²/(4πεmer). Calculate the speed of an electron orbiting at the Bohr radius, ˜Â = 0.053 nm. ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) and of a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour. iii) Compare the wavelength for the electron that you obtain in (ii) with the circumference of the orbit. Comment on this comparison. Explain briefly what it implies about the other possible orbits of the Bohr model and how the higher orbits might be predicted.

5. A microscopic oscillator has its first and second excited states 0.05 eV and 0.10 eV above the ground-state energy. Calculate the Boltzmann factor for the ground state, first excited state, and second excited state, at room temperature.

19. A rocket is sitting on the launch pad. The engines ignite, and therocket begins to rise straight upward, picking up speed as it goes. Atabout 1000 m above the ground the engines shut down, but the rocketcontinues straight upward, losing speed as it goes. It reaches the top ofits fl ight path and then falls back to earth. Ignoring air resistance, decide which one of the following statements is true. (a) All of the rocket’smotion, from the moment the engines ignite until just before the rocketlands, is free-fall. (b) Only part of the rocket’s motion, from just after theengines shut down until just before it lands, is free-fall. (c) Only the rocket’s motion while the engines are fi ring is free-fall. (d) Only the rocket’smotion from the top of its fl ight path until just before landing is free-fall.(e) Only part of the rocket’s motion, from just after the engines shut downuntil it reaches the top of its fl ight path, is free-fall.