# “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.
Solution:
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).
Solution:
Problem 3: Determine the wavelength of a 20 eV electron.
Solution:
Problem 4: An alpha particle (doubly ionized helium) is ejected from the nucleus of a
radium nuclei with 5.78 MeV of kinetic energy.
a)
What is the de Broglie wavelength of this particle?
b)
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?
```