De broglie wavelength multiple choice question

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sarah99630
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whats the concept/rule behind this? So I can answer questions on DB wavelengths in the future? also any link or notes that has this explained would be appreciated. ThanksName:  image-d63d0c6f-539f-4fc3-9f86-431707ff6bd31949625300-compressed.jpg.jpeg
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Bukalemun123
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you have to approximate the mass of the tennis ball and answer accordingly.
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K-Man_PhysCheM
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(Original post by sarah99630)
whats the concept/rule behind this? So I can answer questions on DB wavelengths in the future? also any link or notes that has this explained would be appreciated. ThanksName:  image-d63d0c6f-539f-4fc3-9f86-431707ff6bd31949625300-compressed.jpg.jpeg
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The de Broglie wavelength is a consequence of extending wave-particle duality to any particle/object, so that any particle/object can be assigned a wavelength equivalent to how it behaves as a wave.

The de Broglie equation is \lambda = \dfrac{h}{p},

where \lambda is the wavelength, h is the Planck constant (equal to 6.63 \times 10^{-34} \mathrm{Js}) and p is the momentum of the particle.

Photons don't have mass, but you can use the equation to find the momentum of a photon. Momentum clearly isn't just "mass times velocity" anymore (since 0 mass would mean 0 momentum, but photons do have momentum). But for particles that have mass, the momentum can be calculated by the product of mass and velocity.

Now, in this question you are told that the de Broglie wavelength of a tennis ball is 1 \times 10^{-33} \mathrm{m}.

That is very small. To give you an idea, the spacing between atoms in a crystal lattice is about 1 \times 10^{-10} \mathrm{m}.

Now remember, waves diffract best when they pass through gaps that have a similar width to their wavelength. Clearly no gap will be as small as the tennis ball's de Broglie wavelength, so tennis balls cannot diffract through gaps.

In fact, at such a short wavelength, tennis balls are basically defined to a particular spot (unlike waves, that are spread out over an area). So what type of properties should tennis balls display: particle or wave?
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sarah99630
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(Original post by Bukalemun123)
you have to approximate the mass of the tennis ball and answer accordingly.
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sarah99630
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(Original post by K-Man_PhysCheM)
The de Broglie wavelength is a consequence of extending wave-particle duality to any particle/object, so that any particle/object can be assigned a wavelength equivalent to how it behaves as a wave.

The de Broglie equation is \lambda = \dfrac{h}{p},

where \lambda is the wavelength, h is the Planck constant (equal to 6.63 \times 10^{-34} \mathrm{Js}) and p is the momentum of the particle.

Photons don't have mass, but you can use the equation to find the momentum of a photon. Momentum clearly isn't just "mass times velocity" anymore (since 0 mass would mean 0 momentum, but photons do have momentum). But for particles that have mass, the momentum can be calculated by the product of mass and velocity.

Now, in this question you are told that the de Broglie wavelength of a tennis ball is 1 \times 10^{-33} \mathrm{m}.

That is very small. To give you an idea, the spacing between atoms in a crystal lattice is about 1 \times 10^{-10} \mathrm{m}.

Now remember, waves diffract best when they pass through gaps that have a similar width to their wavelength. Clearly no gap will be as small as the tennis ball's de Broglie wavelength, so tennis balls cannot diffract through gaps.

In fact, at such a short wavelength, tennis balls are basically defined to a particular spot (unlike waves, that are spread out over an area). So what type of properties should tennis balls display: particle or wave?
Particle. Hmm that makes sense now. Thank you very much. Lifesaver
So I guess we just had to use the value being too small regardless of which object they used? Like if they said something really tiny?
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K-Man_PhysCheM
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(Original post by sarah99630)
Particle. Hmm that makes sense now. Thank you very much. Lifesaver
So I guess we just had to use the value being too small regardless of which object they used? Like if they said something really tiny?
Not really. Small particle with little mass will have low momentum (relative to more massive particles with the same velocity), and so they will (generally) have longer de Broglie wavelengths. So they would behave more like waves. For instance, if they gave you an electron with de Broglie wavelength 1\times 10^{-9} \mathrm{m}, then it would diffract through a crystal lattice, so would show wave behaviour at the nanoscale, but discrete particle behaviour in bigger scales (eg in the scale we experience in our day-to-day lives).

Then massless particles, like photons, generally have the longest de Broglie wavelengths (eg visible light is about 650 nm, or 6.5\times 10^{-7}\mathrm{m}). So light behaves both like a wave and a particle in our day-to-day lives (eg light diffracts through really small gaps, but the photoelectric effect implies light is made up of discrete particles).

But the general tactic for multiple choice questions is to eliminate the options that definitely can't be right (eg there is no way a tennis ball could travel at the speed of light, since only massless particles can), and then select the most sensible option. It should be intuitive that a tennis ball behaves like a particle: it doesn't diffract through your tennis racket when you strike it!
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sarah99630
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(Original post by K-Man_PhysCheM)
Not really. Small particle with little mass will have low momentum, and so they will have longer de Broglie wavelengths. So they would behave more like waves. For instance, if they gave you an electron with de Broglie wavelength 1\times 10^{-9} \mathrm{m}, then it would diffract through a crystal lattice, so would show wave behaviour at the nanoscale, but discrete particle behaviour in bigger scales (eg in the scale we experience in our day-to-day lives).

Then massless particles, like photons, generally have the longest de Broglie wavelengths (eg visible light is about 650 nm, or 6.5\times 10^{-7}\mathrm{m}). So light behaves both like a wave and a particle in our day-to-day lives (eg light travels in straight lines, like particles being projected, but light also diffracts through really small gaps).

But the general tactic for multiple choice questions is to eliminate the options that definitely can't be right (eg there is no way a tennis ball could travel at the speed of light, since only massless particles can), and then select the most sensible option. It should be intuitive that a tennis ball behaves like a particle: it doesn't diffract through your tennis racket when you strike it!
Ahh yesss thank you so much. I appreciate it!
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Eimmanuel
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(Original post by sarah99630)
whats the concept/rule behind this? So I can answer questions on DB wavelengths in the future? also any link or notes that has this explained would be appreciated. Thanks

https://cnx.org/contents/[email protected]

https://cnx.org/contents/[email protected]

https://cnx.org/contents/[email protected]

https://cnx.org/contents/[email protected]
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sarah99630
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wow not all heroes wear capes...thank you VERY much!!
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Eimmanuel
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(Original post by K-Man_PhysCheM)
Not really. Small particle with little mass will have low momentum, and so they will have longer de Broglie wavelengths. …
The so-called “low momentum” is not really low momentum. It depends on what are you comparing with.


(Original post by K-Man_PhysCheM)
… So light behaves both like a wave and a particle in our day-to-day lives (eg light travels in straight lines, like particles being projected, but light also diffracts through really small gaps). …
“Light travels in straight lines, like particles being projected” is incorrect.

Light is manifested as “particle” when we deal with Compton effect and photoelectric effect.

We don’t need to consider light as a particle to describe light travels in a straight line.
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Droneon
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(Original post by sarah99630)
whats the concept/rule behind this? So I can answer questions on DB wavelengths in the future? also any link or notes that has this explained would be appreciated. ThanksName:  image-d63d0c6f-539f-4fc3-9f86-431707ff6bd31949625300-compressed.jpg.jpeg
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What's the correct answer for this?
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Eimmanuel
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(Original post by Droneon)
What's the correct answer for this?
C Does not display wave properties
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K-Man_PhysCheM
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(Original post by Eimmanuel)
The so-called “low momentum” is not really low momentum. It depends on what are you comparing with.




“Light travels in straight lines, like particles being projected” is incorrect.

Light is manifested as “particle” when we deal with Compton effect and photoelectric effect.

We don’t need to consider light as a particle to describe light travels in a straight line.
I know, however this post was a simplification for A-level. By "low momentum", I was implying relative to a more massive object travelling at the same velocity. I should have been more explicit about that.

I should have mentioned the photoelectric effect (though Compton scattering isn't in the AS-level/year 1 syllabus, though it is in second year, for my specification). The "light travels in straight lines like a particle..." was to illustrate a point of wave-particle duality, and was not the argument of the post. I will amend my previous post to be more accurate.

Thanks for checking!
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Droneon
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(Original post by Eimmanuel)
C Does not display wave properties
But if it's de Broglie wavelength can be calculated, how can it not display wave properties?
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Droneon
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(Original post by Droneon)
But if it's de Broglie wavelength can be calculated, how can it not display wave properties?
IK it's not realistic for atennis ball to behave like a wave, but thinking theoretically.
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black1blade
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(Original post by Droneon)
But if it's de Broglie wavelength can be calculated, how can it not display wave properties?
A tennis ball is like 5cm in diameter, many orders of magnitudes above it's debrogile wavelength. When you observe a tennis ball, it has no wave properties.
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m005eman
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[QUOTE=it doesn't diffract through your tennis racket when you strike it![/QUOTE]

I mean that'd be awkward if it did
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