‘If someone tells you that they understand Quantum
Mechanics, they are fooling themselves’.
-Richard Feynman
13.1.5 to 13.1.7

• In 1923 Louis de Broglie suggested that since nature should be symmetrical, that just as waves could exhibit particle properties, then what are considered to be particles should exhibit wave properties.

• Based on this result, the de Broglie hypothesis is that any particle will have an associated wavelength given by p = h /λ
• The waves to which the wavelength relates are called matter waves.
• For a person of 70 kg running with a speed of 5 m/s, the wavelength λ associated with the person is given by:
  h p
 h mv

6 .
63

10

34
( 70 )( 5 )

2

10

36 m
• This wavelength is minute to say the least. However, consider an electron moving with speed of 10 7 m/s, then its associated wavelength is:
  h p
 h mv

6 .
63

10

34
( 9 .
11

10

31
)( 10
7
)

7

10

11 m
Although small, this is measurable.

• In 1927 Clinton Davisson and
Lester Germer who both worked at the Bell Laboratory in New Jersey, USA, were studying the scattering of electrons by a nickel crystal. A schematic diagram of their apparatus is shown.

• Their vacuum system broke down and the crystal oxidized. To remove the oxidization, Davisson and
Germer heated the crystal to a high temperature. On continuing the experiment they found that the intensity of the scattered electrons went through a series of maxima and minima the electrons were being diffracted. The heating of the nickel crystal had changed it into a single crystal and the electrons were now behaving just as scattered Xrays do.
• Effectively, that lattice ions of the crystal act as a diffraction grating whose slit width is equal to the spacing of the lattice ions.

• Davisson and Germer were able to calculate the de Broglie wavelength
λ of the electrons from the potential difference V through which they had been accelerated.
• They knew the spacing of the lattice ions from X-ray measurements and so were able to calculate the predicted diffraction angles for a wavelength equal to the de Broglie wavelength of the electrons. The predicted angles were in close agreement with the measured angles and the de Broglie hypothesis was verified – particles behave as waves.

1. Calculate the de Broglie wavelength of an electron after acceleration through a potential difference of 75 V.

2. Determine the ratio of the de Broglie wavelength of an electron to that of a proton accelerated through the same magnitude of potential difference.

• Tsokos
– Page 395
• Questions 1 to 11