PHGN 300 Homework #7

PHGN 300 Homework #7
1) Find the de Broglie wavelength for each of the following electrons with the specified kinetic energy:
electron of 20 keV in a TV tube,
orbiting electron of 13.6 eV in a hydrogen atom,
orbiting electron of 91 keV in a lead atom
electron of 100 GeV in a particle accelerator
a 300 gram baseball traveling at 95 miles per hour
2) An electron initially at rest is accelerated across a potential difference of 3000 volts. What are its
wavelength, momentum, kinetic energy, and total energy?
3) The nucleus of the aluminum atom has a diameter of 7.2x10-15 m. Consider one of the protons in this
nucleus. The uncertainty in the position of this proton is necessarily less than 7.2x10-15m. What is the
minimum uncertainty in its velocity and momentum?
4) In an electron microscope we wish to study particles of diameter about 0.10 µm (about 1000 times
the size of a single atom). (a) What should be the de Broglie wavelength of the electrons? (b) Through
what potential difference should the electrons be accelerated to have that de Broglie wavelength?
5) Krane Ch5 #8
6) For the infinite square-well potential, find the probability that a particle in its ground state is in each
third of the one-dimensional box (of length L) .
Extra Credit
Krane 4-20