Name _________________________________
Rutherford, Bohr and DeBroglie
I. Rutherford Experiment (c. 1911)
What he did: He shot alpha particles (q = +2e) into thin gold foil.
What he expected: He thought that the alpha particles would fly mostly
straight through. Everyone believed that charge in matter was uniformly
distributed, like “plum pudding”.
What actually happened: most of the alphas went straight through, but some of them
were deflected at large angles, some even coming straight back.
What it showed: (1) Matter is mostly empty space. (2) There are small, very dense
concentrations of positive charge which must have repelled the alphas. We call
these concentrations the nucleus.
II. Bohr Model of the Atom (1913 )
Two Problems that it solved:
1) Why do excited atoms produce discrete spectral lines instead of
emitting all colors?
2) Accelerating charged particles give off radiation. As the
electrons orbit the nucleus -- thus undergoing centripetal
acceleration, why don’t they lose energy and fall into the nucleus?
Solution: Bohr made up some rules which “solved” these
problems and fit the data. He had no idea why they worked.
Bohr’s postulates
i) Electrons travel in circular orbits around the nucleus.
ii) Only certain radii are allowed.
iii) When an electron orbits, no energy is radiated.
iv) An atom emits energy (in the form of a photon) when an
electron falls into a lower orbit.
v) An atom must absorb energy (in the form of a photon) for an
electron to go into higher orbit.
III. DeBroglie’s Wave Model of Matter (1923)
Fact: light behaves sometimes like a wave, sometimes like a particle.
Fact: It’s weird that the electrons can only orbit at certain radii, as Bohr
showed. After all, we can send up satellites into any orbit we want. There are
no “forbidden orbits” for satellites; why should there be for electrons?
DeBroglie combined these ideas into one unique hypothesis: Maybe matter
sometimes behaves like a wave! DeBroglie imagined the electron to be a
wave, surrounding the nucleus in a circular, standing wave pattern.
In DeBroglie’s view, the electron didn’t orbit; it vibrated as a wave. When two people shake a coil, only certain standing
wavelengths can be produced. Similarly, only certain electron wavelengths (and thus energies) are allowed.
DeBroglie’s equation for the wavelength of matter:
!=
h
mv
[continued -- practice problems on next page]
Bohr & DeBroglie practice problems
[some answers at bottom of page]
BOHR
1) The diagram at right shows the energy levels for the electron
in the hydrogen atom.
a) When an electron falls from the n = 2 orbital to the ground
state (n = 1), what is the energy of the photon that is emitted?
b) Compute the frequency of the photon emitted in (a).
c) Compute the wavelength of the photon emitted in (a).
d) If the electron is in the ground state, can the atom absorb a photon
whose energy is 10.2 eV?
e) How much energy is needed to “ionize” (remove) the electron of
hydrogen when it’s in its ground state?
f) If the electron is in the ground state and a photon whose energy is
8.4 eV collides with the atom, circle the one true statement:
( # ) The atom may absorb the photon, sending the electron to a higher energy level.
( $ ) The photon cannot be absorbed. The photon will go right through the atom or bounce off, but it can’t be absorbed.
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g) Look at Bohr’s 5 postulates on the other page. Two of them violated the laws of physics that were known in Bohr’s
day. Which two?
DeBROGLIE
2) To observe the “wavelength” of an electron, in 1927 Davisson & Germer sent a beam of electrons having speed
4.3x106 m/s through the “slits” provided by an atomic crystal having spacing 0.91x10-10 m. Because the wavelength of
the electrons was similar to the spacing of the slits, the electron beam produced an interference pattern just like what
we’ve seen before with light. The electrons behaved like waves. Compute the DeBroglie wavelength of the electrons.
3(a) Compute the “wavelength” of a 0.300 kg baseball going 20 m/s. You can think of this wavelength as a measure of
the “blurriness” of the baseball.
b) How slow would the baseball have to be traveling to have a wavelength of 1 cm?
c) If a baseball is sitting at rest on the table (v = 0 m/s) why don’t we observe the wave nature of the baseball? Why
doesn’t the baseball appear all spread out?
Answers: 1(a) 10.2 eV (b) 2.46x101 5 Hz (c) 1.22x10-7 m (d), (e), (f) ? (2) 1.7x10-10 m
3(a) 1.10x10-34 m. This is 10 million trillion times smaller than the diameter of an atomic nucleus.
b) 2.2x10-31 m/s (c) an important question