8.5 (a) Apply the Onsager's quantization condition (8.39) to the orbits of free electron levels and show that it leads directly to the free electron levels (8.26) if y= 1/2. (b) Derive an expression for the degeneracy of Landau levels in the case of a two- dimensional free electron gas. Show that the degeneracy is equal to the number of zero-field free electron levels with a given k₂, and with k, and k, within a planar region of area AS given by (8.29). 8.6 An electron in sodium at the Fermi level moves initially in the xy-plane. Calculate the radius of its cyclotron orbit when a magnetic field of 1 T is applied. What is the ratio of the orbit area in real space to that in k-space?

Here's how gym membership works for a potential customer: If the customer decides to join the gym, she will pay J on day 0. Then, she can use the gym starting the next day for 5 days (1; 2; 3; 4; 5), paying an additional F on each day she visits. If she goes to the gym on any given day, it costs her (10+ F) that day, but beneÖts her 30 the next day. In other words, her "costs" are a sum of her psychic costs (10) and actual Onancial costs (F). Assume that, when indi§erent, the individual will go to the gym. (a) Suppose the potential customer is a standard exponential discounter with a discount factor of = 12. If gym membership was free (i.e. J = 0 and F = 0) would she join the gym? If so, how many days would she actually go? (b) Suppose the gym did not charge a joining fee. How high could it set the usage fee? What would its revenues from this customer be? (c) Suppose instead the gym decided not to charge a usage fee. How high could it set the joining fee? [Hint: To Ögure out the…

The consumption rate of electricity, in kW/h has increased, on average, at 4.5% per year. If it continues to increase at this rate indefinitely, find the number of years before the electric companies will need to double their generating capacity The electric company will need to double their generating capacity about every years. (Do not round until the final answer. Then round to the nearest tenth as needed)

Evaluate the dot product A - Bif A = 2i +7j and B = 7i – 5j. ? A-B= Submit Request Answer Part B Evaluate the dot product A - Bif à = 2î – 7j and B = 5i +7j.