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Homework Assignment in Physics: Optics and Waves - Prof. David Ginger Jr, Assignments of Quantum Chemistry

University of Washington (UW) - SeattleQuantum Chemistry
Prof. David Ginger Jr

A physics homework assignment focusing on optics and waves. The assignment includes problems related to photon energy, human eye sensitivity, microscope resolution, and wave equations. Students are required to use maple software for calculations. Topics covered include photon energy, wavelength, human eye detection, microscope resolution, and wave equations.

Typology: Assignments

Pre 2010

Uploaded on 03/18/2009

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Homework 1: Due MONDAY Oct. 3 at 5pm in my mailbox
For some of you this will be review. For others parts will be new. You should still work
all of it.
Note: All Levine Problems reference the 5th Edition
Graduate students should request their download code for Maple ASAP. Download and
install it on your PC.
http://www.washington.edu/computing/software/sitelicenses/maple/
I STRONGLY recommend you run it in “Classic Worksheet Maple 9” mode rather than
the JAVA worksheet mode (it is 10-100X faster). Undergraduates are encouraged to
consider obtaining a student copy, or finding a campus lab that is open during hours
compatible with their class schedule.
Levine Problems: (Use Maple whenever possible)
Problems: 1.7, 1.8, 1.29
Additional Problems: from basic units to Diff Eqns and Fourier Series, don’t judge
them all by the first few
1) a) Calculate ν, and the energy (in eV) per photon for radiation of wavelength 500
nm.
b) What is the wavelength of a photon with twice this energy?
c) For the waves in (a) and (b) express the units in terms of reciprocal centimeters
(cm-1 [sometimes still called wavenumbers])
d) What ‘color’ are these photons?
e) What is the energy in eV of a photon that would be absorbed by a C=O
carbonyl stretch?
f) What kind of instrument would you use to record a spectrum containing the
peak in part e)?
g) What are general (easily memorized) formulae for converting
i) a photon energy in nm to an energy in eV?
ii) a photon energy in cm-1 to an energy in eV?
2) Suppose that a 100W source radiates 600 nm light uniformly in all directions.
Assuming that the human eye can detect this light if only 20 photons per second
enter a dark-adapted eye with a 7-mm diameter pupil. How far from the source
can the light be detected under these conditions? Why do you think can’t we see
this far in the “real world”?
pf2

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Download Homework Assignment in Physics: Optics and Waves - Prof. David Ginger Jr and more Assignments Quantum Chemistry in PDF only on Docsity!

Homework 1 : Due MONDAY Oct. 3 at 5pm in my mailbox

For some of you this will be review. For others parts will be new. You should still work all of it.

Note: All Levine Problems reference the 5 th^ Edition

Graduate students should request their download code for Maple ASAP. Download and install it on your PC. http://www.washington.edu/computing/software/sitelicenses/maple/ I STRONGLY recommend you run it in “Classic Worksheet Maple 9” mode rather than the JAVA worksheet mode (it is 10-100X faster). Undergraduates are encouraged to consider obtaining a student copy, or finding a campus lab that is open during hours compatible with their class schedule.

Levine Problems: (Use Maple whenever possible)

Problems: 1.7, 1.8, 1.

Additional Problems : from basic units to Diff Eqns and Fourier Series, don’t judge them all by the first few

  1. a) Calculate ν, and the energy (in eV) per photon for radiation of wavelength 500 nm. b) What is the wavelength of a photon with twice this energy? c) For the waves in (a) and (b) express the units in terms of reciprocal centimeters (cm-1^ [sometimes still called wavenumbers]) d) What ‘color’ are these photons? e) What is the energy in eV of a photon that would be absorbed by a C=O carbonyl stretch? f) What kind of instrument would you use to record a spectrum containing the peak in part e)? g) What are general (easily memorized) formulae for converting i) a photon energy in nm to an energy in eV? ii) a photon energy in cm -1^ to an energy in eV?

  2. Suppose that a 100W source radiates 600 nm light uniformly in all directions. Assuming that the human eye can detect this light if only 20 photons per second enter a dark-adapted eye with a 7-mm diameter pupil. How far from the source can the light be detected under these conditions? Why do you think can’t we see this far in the “real world”?

  1. Qualitatively explain what limits the resolution of an optical microscope. Explain why an electron microscope can image objects with higher-resolution than an optical microscope? Estimate (with a De Broglie calculation) the best resolution that could be expected from a transmission electron microscope (TEM) that accelerates electrons with a potential of 200 kV assuming the microscope optics are ‘perfect.’ If you don’t know special relativity you have the option of ignoring relativistic effects for this problem--although these electrons are traveling fast enough that an accurate calculation would account for special relativity. In the real world TEM resolution is limited by aberrations in the electromagnetic lenses, vibrations and other practical considerations.

  2. The equation of motion for the classical simple harmonic oscillator is given by:

2 2 ()^0

2

  • xt = dt

d x

ω (where ω = mk )

Solve this equation to find x(t) for the time t=0 initial (boundary) conditions x(0)=A, x’^ (0)=v (^0)

5) The classical 1D wave equation (i.e. which described the motion of a 1D guitar string) is:

2

2 2 2

t

xt x c

xt ∂

Where ψ ( x , t )is the classical wave-function giving the amplitude of the wave at position

x and time t, and c is the speed of the wave.

5a) Use the method of the separation of variables to find the solution to the classical wave equation.

5b) Consider a string with c=1 m/s with ends fixed a x=0 and x=6π m. At time t=0, someone stretches the string into the square bump described by: ψ = 0 |x-3π| > π/2 m

π

ψ

= |x-3π| < π/2 m

Given the solution to the classical wave equation. Find the coefficients of the Fourier series solution describing this initial state. Plot the square of the coefficients versus frequency.

5c) Use the Maple animate command to generate a movie of the resulting wave motion.