3.7 Sample Test Problems
- What is the deBroglie wavelength of an electron with 13.6 eV of kinetic energy? What is the
deBroglie wavelength of an electron with 10 MeV of kinetic energy?
Answer
13.6 eV is much less thanmc^2 = 0. 511 MeV so this is non-relativistic.
p^2
2 m
= 13. 6
p^2 c^2
2 mc^2
= 13. 6
pc =
√
2 mc^2 (13.6)
λ =
h
p
=
2 π ̄h
p
=
2 π ̄hc
pc
=
2 π ̄hc
√
2 mc^2 (13.6)
=
2 π(1973eV ̊A)
√
2(0. 511 × 106 eV)(13. 6 eV)
≈ 3. 33 ̊A
10 MeV is much bigger thanmc^2 for an electron so it is super-relativistic and we can use
E=pc.
λ=
2 π ̄hc
pc
=
2 π(197.3)MeV F)
10 MeV
≈ 120 F
- What is the DeBroglie wavelength for each of the following particles? The energies given are
the kinetic energies.
a) a 10 eV electron
b) a 1 MeV electron
c) a 10 MeV proton
- A 2 slit electron diffraction experiment is set up as (not) shown below. The observed electron
intensity distribution is plotted in the figure. Now an intense light source is introduced near the
two slits. With this light, it can be ”seen” which slit each electron goes through. Qualitatively
plot the new electron intensity distribution from each slit and from the 2 slits combined. What
is the condition on the wavelength of the light for this effect to occur?
- What is the DeBroglie wavelength for each of the following particles? The energies given are
the kinetic energies.
a) a 1 eV electron
b) a 10^4 MeV proton
- What K.E. must a Hydrogen atom have so that its DeBroglie wavelength is smaller than the
size of the atom? (Factors of 2 are not important.)
- Calculate the DeBroglie wavelength for (a) a proton with 10 MeV kinetic energy, (b) An
electron with 10 MeV kinetic energy, and (c) a 1 gram lead ball moving with a velocity of 10
cm/sec (one erg is one gram cm^2 /sec^2 ). Be sure to take account of relativity where needed.
7.
