Physics 10: Additional HW 7 Problems
In addition to the problems from the book: 26.E.3, 26.E.4, 26.E.10,
26.E.14, 26.E.38, 26.P.4, 31.E.4, 31.E.9, the following four problems are a
part of the required homework.
- Your cell phone likely operates at a frequency of around 1.1 GHz
(1.1×109 Hz). Convert this to a wavelength, and take a
quarter of that to arrive at the ideal size for a cell phone antenna.
What is the antenna size you get? Draw this length on the page (hint: if
it is hard to draw, you've done something wrong).
- If you want to see individual atoms with visible light, you may
be disappointed. In order to resolve something like an atom, the effective
wavelength of the probing source must be smaller than the scale of the
atom. Visible light has a wavelength around 550 nm (nanometers). Atoms
are typically about a tenth of a nanometer in scale. So it won't work.
All we can hope to do with visible light is resolve large blobs of atoms.
About how many atoms across would the smallest blob resolvable to visible
light be? Any smaller than this and a visible-light microscope is of no
use.
- To see things smaller than the wavelength of light, we often use
electrons as the probe (electron microscope), which via particle-wave
duality have an effective wavelength (called de Broglie wavelength) that
is λ = h/p, where h = 6.63×10-34
J·s is Planck's constant, and p = mv is the particle momentum.
If the mass of an electron is m = 9×10-31
kg, how fast must it be traveling to probe a size scale of an atom
(10-10 meters)? Make sure the units work out. The speed works
out to be quite significant (more than 1% the speed of light!). You can
imagine this is a disruptive way to probe small scalesin fact, it's
too disruptive to really work: we use other means to see the atomic scale.
- Explain why the Heisenberg uncertainty principle is not a matter of
sloppy measurements, but relates to a fundamental limit to how well one can
simultaneously know a particle's position and momentum (velocity). (Note:
this is not entirely unrelated to the previous problem.)