The Wave Nature of Matter (7.2.1) Flashcards
• In 1924, de Broglie postulated that matter, just like light, can have both wave and
particle properties.
• In 1924, de Broglie postulated that matter, just like light, can have both wave and
particle properties.
• Electrons produce an interference pattern when passed through a crystal.
• Electrons produce an interference pattern when passed through a crystal.
• Electrons are standing waves with quantized energy levels.
• Electrons are standing waves with quantized energy levels.
In 1924, de Broglie postulated that matter, just like
light, can have both wave and particle properties.
Specifically, de Broglie calculated that the
wavelength (λ) of a particle is equal to Planck’s
constant (h) divided by the momentum (ρ) of the
particle. Momentum is equal to mass multiplied by
velocity. When two particles with the same mass
travel at different velocities, the slower particle has a
longer wavelength. When two particles with
different masses travel at the same velocity, the
larger particle has a smaller wavelength.
Using this formula, the de Broglie wavelength of
an electron traveling at 1.0 x 106
m/s can be
calculated. Planck’s constant is 6.63 x 10–34 kg•m2
,
and the mass of an electron is 9.109 x 10–31 kg.
Plugging in these values yields a wavelength of
7.3 x 10–10 m. This is on the order of the size of an
atom.
In 1927, Davisson and Germer proved that particles
(specifically electrons) have wave properties.
When waves are passed through small slits, an
interference pattern is formed. Davisson and
Germer passed electrons through a crystal, and
found an interference pattern. The wave nature of
the electron was exactly as de Broglie had
predicted.
In 1924, de Broglie postulated that matter, just like
light, can have both wave and particle properties.
Specifically, de Broglie calculated that the
wavelength (λ) of a particle is equal to Planck’s
constant (h) divided by the momentum (ρ) of the
particle. Momentum is equal to mass multiplied by
velocity. When two particles with the same mass
travel at different velocities, the slower particle has a
longer wavelength. When two particles with
different masses travel at the same velocity, the
larger particle has a smaller wavelength.
Using this formula, the de Broglie wavelength of
an electron traveling at 1.0 x 106
m/s can be
calculated. Planck’s constant is 6.63 x 10–34 kg•m2
,
and the mass of an electron is 9.109 x 10–31 kg.
Plugging in these values yields a wavelength of
7.3 x 10–10 m. This is on the order of the size of an
atom.
In 1927, Davisson and Germer proved that particles
(specifically electrons) have wave properties.
When waves are passed through small slits, an
interference pattern is formed. Davisson and
Germer passed electrons through a crystal, and
found an interference pattern. The wave nature of
the electron was exactly as de Broglie had
predicted.
A standing wave vibrates in a fixed region.
Standing waves (such as guitar strings) can only
have certain frequencies (the fundamental,
second harmonic, third harmonic, etc). The
frequencies are therefore quantized.
Electrons are standing waves. If the wave
reinforces itself (such as in the example on the left),
that energy level is permitted. However, if the wave
does not reinforce itself (such as the example on the
right), that energy level is not permitted.
The energy of the electron is quantized because of
the wave properties associated with it.
A standing wave vibrates in a fixed region.
Standing waves (such as guitar strings) can only
have certain frequencies (the fundamental,
second harmonic, third harmonic, etc). The
frequencies are therefore quantized.
Electrons are standing waves. If the wave
reinforces itself (such as in the example on the left),
that energy level is permitted. However, if the wave
does not reinforce itself (such as the example on the
right), that energy level is not permitted.
The energy of the electron is quantized because of
the wave properties associated with it.
A string has a length of 84 cm. The string is stretched taut, and both ends are restricted to be nonmoving. Touching the string at which of the following points will not produce a standing wave when the string is plucked?
36 cm from one end (C)
Which of these particles will have the shortest de Broglie wavelength?
A proton with a velocity of 9.0 × 10^5 m / s (B)
What will happen when two identical waves that are out of phase with each other combine?
The resulting wave will have zero amplitude. (A)
Suppose a beam of neutrons is fired at a crystal that has a spacing of 0.215 nm between atoms. Photographic film is used to record the places where the neutrons come through the crystal.
Which of the following is the best estimate of the slowest speed at which the neutrons can be fired at the crystal and still result in an interference pattern on the film? (The mass of a neutron is 1.67 × 10−27 kg.)
1.85 × 10^3 m / s (B)
What would the results of Davisson and Germer’s experiment have been if they had used X-rays with a wavelength of 1 angstrom instead of a beam of electrons? (In their experiment, electrons were fired at a crystal of magnesium oxide, and photographic film was used to record the places where the electrons came through the crystal.)
An interference pattern would have been seen on the film. (B)
In which of the following ways does an electron in a hydrogen atom differ from a radio wave?
(The mass of an electron is 9.11 × 10^−31 kg.)
The electron will have a slower velocity. (B)
An atom of helium
has a de Broglie wavelength of
4.3 × 10^−12 meters.
What is its velocity?
2.3 × 10^4 m / s (B)
Which of the following is the best explanation of why the energy of electrons is quantized?
Wavelengths of electrons that result in destructive interference are disallowed near the nucleus. (D)
A molecule of oxygen gas (O2 ) has a velocity of 2800 m / s.
What is its de Broglie wavelength?
4.5 × 10^−12 m (A)
What is a Propagating Wave?
A wave that moves through space.
