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5 min read•june 18, 2024
Daniella Garcia-Loos
Saarah Hasan
Daniella Garcia-Loos
Saarah Hasan
From previous lessons, we already know that light behaves as both a particle and a wave. In 7.5, we’re going to expand on this duality.
The coexistence of particle and wave properties for fundamental particles is known as wave-particle duality. On a small scale, particles can showcase the properties of waves. Think back to double-slit experiments: if a stream of particles were traveled through the slit, they would diffract. Waves can also showcase properties of particles; photons have particle properties like momentum and energy, which relate to their frequency and wavelength.
In the 1920s, a physicist named Arthur Compton conducted experiments that showed that when an X-ray photon collides with an electron, the collision obeys that law of conservation of momentum. In this momentum interaction, known as the Compton effect, the scattered photon has a lower frequency than the incident photon.
p=h/λ
This raised a question: if an electromagnetic wave, can a particle of matter behave like a wave? A physicist named Louis de Broglie suggested that the answer was yes. Since a photon’s momentum is p=h/λ, the wavelength can be rearranged to
λ=h/p
If the momentum of a particle (p=mv) is big enough to overcome Planck’s constant, a significant wavelength can be observed. For this to happen, the mass has to be extremely small (on the atomic scale). The equation for the de Broglie wavelength of a particle becomes:
λ=h/mv
Wave-particle duality is the concept that particles, such as electrons and photons, can exhibit both wave-like and particle-like behavior. It is a fundamental principle of quantum mechanics that has been confirmed by numerous experiments.
Here are some key points about wave-particle duality:
Let's do some practice together:
Electrons in a diffraction experiment are accelerated through a potential difference of 175 V. What's the de Broglie wavelength of these electrons? p=mv ➡️ p=√(2mK) KE=1/2mv^2 λ=h/p=h/√(2mK) =6.6310^-^3^4 Js/√(2(9.1110^-^3^1 kg))[125 eV1.610^-^1^9 J/1 eV] = 9.310^-^1^1 m = 0.093 nm
Relativistic mass-energy equivalence is the concept that the mass of an object increases as its velocity increases. It is a consequence of the theory of relativity and is described by the equation E=mc^2, where E is energy, m is mass, and c is the speed of light.
Here are some key points about relativistic mass-energy equivalence:
Interference and diffraction are phenomena that are observed in waves, such as light waves or sound waves. They are not observed in particles, such as electrons or atoms.
Here are some key points about why only waves display interference and diffraction:
1, An atomic particle of mass m moving at speed v is found to have wavelength λ. What is the wavelength of a second particle with a speed 3v and the same mass? A) (1/9) λ
B) (1/3) λ
C) λ
D) 3 λ
E) 9 λ
2.A very slow proton has its kinetic energy doubled. What happens to the protons corresponding de Broglie wavelength? A) the wavelength is decreased by a factor of √2 B) the wavelength is halved C) there is no change in the wavelength D) the wavelength is increased by a factor of √2 E) the wavelength is doubled.
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5 min read•june 18, 2024
Daniella Garcia-Loos
Saarah Hasan
Daniella Garcia-Loos
Saarah Hasan
From previous lessons, we already know that light behaves as both a particle and a wave. In 7.5, we’re going to expand on this duality.
The coexistence of particle and wave properties for fundamental particles is known as wave-particle duality. On a small scale, particles can showcase the properties of waves. Think back to double-slit experiments: if a stream of particles were traveled through the slit, they would diffract. Waves can also showcase properties of particles; photons have particle properties like momentum and energy, which relate to their frequency and wavelength.
In the 1920s, a physicist named Arthur Compton conducted experiments that showed that when an X-ray photon collides with an electron, the collision obeys that law of conservation of momentum. In this momentum interaction, known as the Compton effect, the scattered photon has a lower frequency than the incident photon.
p=h/λ
This raised a question: if an electromagnetic wave, can a particle of matter behave like a wave? A physicist named Louis de Broglie suggested that the answer was yes. Since a photon’s momentum is p=h/λ, the wavelength can be rearranged to
λ=h/p
If the momentum of a particle (p=mv) is big enough to overcome Planck’s constant, a significant wavelength can be observed. For this to happen, the mass has to be extremely small (on the atomic scale). The equation for the de Broglie wavelength of a particle becomes:
λ=h/mv
Wave-particle duality is the concept that particles, such as electrons and photons, can exhibit both wave-like and particle-like behavior. It is a fundamental principle of quantum mechanics that has been confirmed by numerous experiments.
Here are some key points about wave-particle duality:
Let's do some practice together:
Electrons in a diffraction experiment are accelerated through a potential difference of 175 V. What's the de Broglie wavelength of these electrons? p=mv ➡️ p=√(2mK) KE=1/2mv^2 λ=h/p=h/√(2mK) =6.6310^-^3^4 Js/√(2(9.1110^-^3^1 kg))[125 eV1.610^-^1^9 J/1 eV] = 9.310^-^1^1 m = 0.093 nm
Relativistic mass-energy equivalence is the concept that the mass of an object increases as its velocity increases. It is a consequence of the theory of relativity and is described by the equation E=mc^2, where E is energy, m is mass, and c is the speed of light.
Here are some key points about relativistic mass-energy equivalence:
Interference and diffraction are phenomena that are observed in waves, such as light waves or sound waves. They are not observed in particles, such as electrons or atoms.
Here are some key points about why only waves display interference and diffraction:
1, An atomic particle of mass m moving at speed v is found to have wavelength λ. What is the wavelength of a second particle with a speed 3v and the same mass? A) (1/9) λ
B) (1/3) λ
C) λ
D) 3 λ
E) 9 λ
2.A very slow proton has its kinetic energy doubled. What happens to the protons corresponding de Broglie wavelength? A) the wavelength is decreased by a factor of √2 B) the wavelength is halved C) there is no change in the wavelength D) the wavelength is increased by a factor of √2 E) the wavelength is doubled.
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