3. [2 pts] [Cylindrical coordinates] State a formula for r in terms of x, y and z 4. [3 pts] [Spherical coordinates] Draw a sketch that illustrates the geometric meaning of p, 6, and o.

12. Which of the following has the largest radius? A) Ве B) С C) О D) F E) Ne

Schrodinger and de Broglie suggested a ‘Wave—particle duality" for small particles—that is, if electromagnetic radiation showed some particle-like properties, then perhaps small punicles might exhibit same wave-like properties. Explain. How does the wave mechanical picture of the atom fundamentally differ from the Bohr model? How do wave mechanical arbitals differ from Bohr’s orbits? What does it mean to say that an orbital represents a probability map for an electron?

Enrico Fermi (1901–1954) was a famous physicist who liked to pose what are now known as Fermi problems, in which several assumptions are made in order to make a seemingly impossible estimate. Probably the most famous example is the estimate of the number of piano tuners in Chicago using the approximate population of the city and assumptions about how many households have pianos, how often pianos need tuning, and how many hours a given tuner works in a year. Another famous example of a Fermi problem is "Caesar's last breath," which estimates that you, right now, are breathing some of the molecules exhaled by Julius Caesar just before he died. The assumptions made are: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The atmosphere is 50 km thick, has an average temperature of 15 °C, and an average pressure of 0.20 atm. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500 mL. Perform the…