“Test Your Knowledge” Problem 1: Solution:

“Test Your Knowledge”
Problem 1: Determine the wavelength of a 0.25 kg baseball moving at 30 m/s.
Step1 - Do we need to use relativity?
Step 2 - Calculate Linear Momentum
Step 3 - Use deBroglie relationship to find wavelength
Problem 2: Determine the wavelength of a 2GeV electron from the Stanford Linear
Accelerator (SLAC).
Problem 3: Determine the wavelength of a 20 eV electron.
Problem 4: An alpha particle (doubly ionized helium) is ejected from the nucleus of a
radium nuclei with 5.78 MeV of kinetic energy.
What is the de Broglie wavelength of this particle?
How does this wavelength compare with the nuclear diameter, which is about
2 x10-14 m?
Problem 5: The electron in a hydrogen atom moves into the excited state n=2 and
remains there for 10-8 s before making a downward transition to the ground state.
Calculate the uncertainty of the energy in the state n=2. Is this a significant correction to
the Bohr theory prediction of -3.39 eV?
Problem 6: We wish to simultaneously measure the wavelength and position of a photon.
Assume that our measurement of wavelength gives  = 600 nm and that our equipment
allows an accuracy of one part in a million in the measurement of .What is the minimum
uncertainty in the position of the photon?