Physics A-level:de Broglie confuses me

Watch
someusernamet
Badges: 9
Rep:
?
#1
Report Thread starter 1 year ago
#1
Why exactly does a particle with more momentum have a shorter wavelength?Surely if it’s got more “oomph” the wavelength travelled by the particle will be greater so the diffraction pattern should be greater(more spread out).

I know that in reality this greater momentum(either through greater mass and/or velocity of the particle) results in a shorter wavelength and therefore smaller spread of lines/spacing of rings in the diffraction pattern but I don’t understand why.I understand the de Broglie wavelength and the relationship between the wavelength,plancks constant and momentum but I’m stuck here.

THANKS FOR ANY HELP BTW
0
reply
Okay123
Badges: 14
Rep:
?
#2
Report 1 year ago
#2
Some things you just don’t question my dude wavelength is inversely proportional to momentum which is mass*velocty so
Wavelength = h/mv so wavelength is inversely proportional to mass/velocity too.
SO higher mass or velocity or momentum also means smaller wavelength, pretty sure the spec don’t want you to know WHY this is the case, just that it IS the case.
Also remember stupid questions like protons not being able to do wave particle bs as good as electrons because they have a larger mass so larger momentum so smaller wavelength making them harder to observe potential patterns
Edit: I just realised I told you what you already know, but that’s the point you don’t need to know anymore, physics is disgusting anyway don’t torture yourself with more knowledge
Last edited by Okay123; 1 year ago
0
reply
GreenCub
Badges: 20
Rep:
?
#3
Report 1 year ago
#3
(Original post by someusernamet)
Why exactly does a particle with more momentum have a shorter wavelength?Surely if it’s got more “oomph” the wavelength travelled by the particle will be greater so the diffraction pattern should be greater(more spread out).

I know that in reality this greater momentum(either through greater mass and/or velocity of the particle) results in a shorter wavelength and therefore smaller spread of lines/spacing of rings in the diffraction pattern but I don’t understand why.I understand the de Broglie wavelength and the relationship between the wavelength,plancks constant and momentum but I’m stuck here.

THANKS FOR ANY HELP BTW
When you consider wave-particle duality, you should think of the photon/electron/whatever it is as having both wave and particle properties.

It doesn't make very much sense to think of a particle moving through space as having a wavelength, since a wavelength is defined as the distance between two adjacent points of equal displacement along a wave. There's no clear way to define this for a particle. The de Broglie equation states that every particle with momentum can exhibit wave properties.

A level physics equation derivations are very questionable sometimes, but this explanation may help you to get a little intuition as to why this works.

You'll be familiar with the equation E=hf which relates energy of a photon to its frequency. Since v=f \lambda for waves, we can write E=hf=\frac{hc}{\lambda} which implies that a photon has wave properties, due to having a wavelength.

There's also a more general equation relating mass and energy, E=mc^2. We can set these equal and show that mc^2=\frac{hc}{\lambda} so mc=\frac{h}{\lambda} and \lambda=\frac{h}{mc}.

You can then deduce that increasing the momentum mc (or more generally, mv) will decrease the wavelength associated with the particle. The wavelength has nothing to do with how much 'oomph' the particle has; the wavelength that you work out using the equation is the wavelength that the particle would have if it were behaving as a wave.
Last edited by GreenCub; 1 year ago
0
reply
Eimmanuel
Badges: 13
Rep:
?
#4
Report 1 year ago
#4
(Original post by GreenCub)
When you consider wave-particle duality, you should think of the photon/electron/whatever it is as having both wave and particle properties.

It doesn't make very much sense to think of a particle moving through space as having a wavelength, since a wavelength is defined as the distance between two adjacent points of equal displacement along a wave. There's no clear way to define this for a particle. The de Broglie equation states that every particle with momentum can exhibit wave properties.

A level physics equation derivations are very questionable sometimes, but this explanation may help you to get a little intuition as to why this works.

You'll be familiar with the equation E=hf which relates energy of a photon to its frequency. Since v=f \lambda for waves, we can write E=hf=\frac{hc}{\lambda} which implies that a photon has wave properties, due to having a wavelength.

There's also a more general equation relating mass and energy, E=mc^2. We can set these equal and show that mc^2=\frac{hc}{\lambda} so mc=\frac{h}{\lambda} and \lambda=\frac{h}{mc}.

You can then deduce that increasing the momentum mc (or more generally, mv) will decrease the wavelength associated with the particle. The wavelength has nothing to do with how much 'oomph' the particle has; the wavelength that you work out using the equation is the wavelength that the particle would have if it were behaving as a wave.
The following paragraph is a flaw.

There's also a more general equation relating mass and energy, E=mc^2. We can set these equal and show that mc^2=\frac{hc}{\lambda} so mc=\frac{h}{\lambda} and \lambda=\frac{h}{mc}.

First of all, you really need to understand conceptually what is the m in the equation of E = mc2. The m in the equation of E = mc2 is the rest mass of the object and photon does not have rest mass. If the “object” does not have rest mass, it can travel at the speed of light c while object such as electrons and protons that has rest mass, cannot travel at the speed of light.



When we want to talk about wave-particle duality, it always better to use

 p = \dfrac{h}{\lambda}

https://en.m.wikipedia.org/wiki/Matter_wave
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Have you experienced financial difficulties as a student due to Covid-19?

Yes, I have really struggled financially (44)
18.57%
I have experienced some financial difficulties (68)
28.69%
I haven't experienced any financial difficulties and things have stayed the same (89)
37.55%
I have had better financial opportunities as a result of the pandemic (30)
12.66%
I've had another experience (let us know in the thread!) (6)
2.53%

Watched Threads

View All