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Problem 1: In class on 2019-09-05 we started to compute the volume and size of a water molecule by

considering the volume of a block of ice. What, roughly, is the volume of 18g of ice, and therefore what, roughly, is the volume of an ice molecule? If you think of the molecule as a cube (yes this is a bad approximation), how big is that cube (how long are the sides of the cube)? Now do the same for an iron atom by considering solid iron, and for a lead atom by considering solid lead.

Problem 2: compute the size of a molecule a different way: imagine that when you drive a car around, the tire leaves a mono-molecular layer of rubber everywhere it goes. sounds crazy, right? but it's close to true:

A typical tire lasts 50,000 miles. go look at a tire and estimate the depth of the tread, and therefore the thickness of the rubber left on the road, on average, over those 50,000 miles. is that thickness reasonable to be mono- molecular?

Problem 3: Piano strings (it turns out) are characterized by a mass m, a length L, and a tension T (force). Find an expression that combines m, L, and T into a quantity with the units of frequency.

Now imagine a piano string has a diameter of D = 1mm, a length of L = 2 m, and is made of steel. What, roughly, is its mass m? And roughly what is the tension T it must have to play middle C? You might have to look up the frequency of middle C on the internets.

Problem 4: Explain in words why you get a "diffraction pattern" when light of one single wavelength (like laser light) goes through a pair of slits separated in space by a many wavelengths. That is, explain the double-slit experiment.

Draw a diagram that shows the slits and the screen and the position on the screen of the central bright (constructive interference) point relative to the two slits. Add to your diagram the positions of the next dark and bright points going away from that central bright point. Label these bright and dark points with the path differences from the two slits.

Problem 5: Imagine that electrons are bound to a metal with a voltage of 2 V (that is, it takes 2 eV of energy to liberate the electron, or the work function is 2 eV). This metal is illuminated with light of different wavelengths: 1 μm, 0.5 μm, and 0.25 μm.

For which wavelengths is it possible for the light to liberate electrons by the photo-electric effect? And, for the wavelengths that can liberate electrons, what are the kinetic energies and speeds of the liberated electrons? Use the classical (1/2) m v2 formula for kinetic energy. Is that formula okay, or should we be using something more relativistically correct?

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