# What is De broglie wavelength: Definition and 150 Discussions

Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave. In most cases, however, the wavelength is too small to have a practical impact on day-to-day activities.
The concept that matter behaves like a wave was proposed by French physicist Louis de Broglie () in 1924. It is also referred to as the de Broglie hypothesis. Matter waves are referred to as de Broglie waves.
The de Broglie wavelength is the wavelength, λ, associated with a massive particle (i.e., a particle with mass, as opposed to a massless particle) and is related to its momentum, p, through the Planck constant, h:

λ
=

h
p

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h

m
v

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{\displaystyle \lambda ={\frac {h}{p}}={\frac {h}{mv}}.}
Wave-like behavior of matter was first experimentally demonstrated by George Paget Thomson's thin metal diffraction experiment, and independently in the Davisson–Germer experiment, both using electrons; and it has also been confirmed for other elementary particles, neutral atoms and even molecules.

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1. ### How do you prove ##\lambda = \frac {2L} {n} ## given only L?

Since I know from the equation the type of particle and the distance L, I thought of equating the first relevant equation to the second equation. Since n = 1, 2, 3 ..., I thought by equating the two equations I could get k = 1, 4, 9... and have the two constants equal each other. The two...

3. ### B What is the nature of de Broglie matter wave? Is it longitudian or transverse?

I just want to elaborate the wave nature of electron from davisson and germer experiment . there is resonance of energy (54 ev)provide to electron for which it show wave like behavior's. give some better explanation for this.
4. ### B Time Dilation & Muon De Broglie Wavelength: Explained

I understand it's experimentally verified muons traveling at relativistic speeds relative to an observer will be observed to have longer half-life than would be observed in the rest frame of the muons, which is explained theoretically by a relativistic time dilation effect. Does this correspond...
5. ### I E=hf for massive particles, but which Energy exactly?

Hi there, I'm a bit confused about the E=hf equation for mass particle(f for frequency), and Lorentz Invariant (E^2 -p^2c^2=m^2c^4). The question is, which energy is it? Total Energy- Kinetic plus Rest, or only kinetic energy. Now, if it's total energy, then you get that a particle at rest...
6. ### I Maximum acceleration of an alpha particle?

I would like to estimate the maximum acceleration (or deceleration) of an alpha particle that is backscattered by a heavy atom, like in Rutherford backscattering. I am interested in the order of magnitude, not in a precise value. I am assuming the collision is elastic. The kinetic energy of the...
7. ### Can a Single Point Grapefruit Create an Interference Pattern?

I tried using lamba = h/p as follows: (6.626 * 10^-34 J *s) / (8 m.s * 0.6 kg) = 1.38041667*10^−34 and then using the small angle approximation sin(alpha) = lamba/d as follows: (1.38041667*10^−34)/(0.6m) = 2.30069444 * 10^−34 then converting to radians with the following: (2.30069444 *...
8. ### A question related to de Broglie wavelength and the Uncertainty Principle

"Now, if an electron has a definite momentum p, (i.e.del p = 0), by the de Broglie relation, it has a definite wavelength.A wave of definite (single) wavelength extends all over space. By Born’s probability interpretation this means that the electron is not localised in any finite region of...
9. E

### When does the wavefunction wavelength equal the De Broglie wavelength?

For instance, in the case of the infinite square well, the wavelength of the wavefunction is \frac{2L}{n}. This also turns out to be the De Broglie wavelength, and and we can find the possible energies directly from the Schrodinger equation, or by using the De Broglie relations. However, if the...
10. ### De Broglie wavelength of an electron

I'm reposting this thread with some editing suggested by fresh_42: 1. Homework Statement Calculate the mass, velocity and the de Broglie wavelength of an electron and an alpha particle, given the kinetic energy K = 2MeV Homework EquationsThe Attempt at a Solution please find attached![/B]...
11. ### De Broglie wavelength of electron and proton

Homework Statement Homework EquationsThe Attempt at a Solution de Broglie wavelength λ of a particle = h /P a) since mass of proton is more than electron and speed is same , momentum of proton is more . De Broglie wavelength of proton will be less . b) wavelengths will be same . c) Using...
12. ### Calculating the frequency of a free electron

I feel like I must be missing something obvious, but I can't figure it out. I have the speed of an electron, and to calculate its frequency i used p = h/λ, then subbed in p =mv and λ= v/f. Giving me the equation f = mv2/h. However, I also could use E = 1/2 mv2 and E = hf to give me the equation...
13. ### Wavefunctions and the de Broglie wavelength

The position wavefunction makes a spatial probability amplitude wave right? And it is the combination of different frequencies My question is that if these frequencies are the spatial frequencies in the debrogile relations
14. ### I Davison-Germer experiment - Bragg condition

Hey, I'm trying to adapt the Bragg condition for the David-Germer experiment, so I can then use their experimental results to show that the measured wavelength is compatible to the wavelength theorized by De Broglie. However I'm having issue with the calculation, any help would be much...
15. ### De – Broglie wavelength of O_2

Homework Statement Homework EquationsThe Attempt at a Solution [/B] De – Broglie wavelength of ## O_2 ## molecule is ## \lambda = \frac h p ## Assuming that the speed of molecule is small enough to take non – relativistic calculation, ## \frac {...
16. ### I A question about a particle's de Broglie wavelength

For electron scattering experiment which measures charge radius of the nucleus, it's said that energies of scattering electrons (or protons) must be such that their wavelength size is of the same order as nuclear dimensions. While i understand why this must be true I'm not entirely sure. My...
17. ### I De Broglie wavelength in non-constant potential?

Hi. Does the de Broglie wavelength have any significance for the wavefunctions of particles in a potential that is non-constant in no region of space? As far as I can see, the solutions of the time-independent Schrödinger equation are only sinusoidal if ##E>V=const##. This is enough to derive...
18. ### B De Broglie Wavelength & Classical EM Wavelength Comparison

Under what condition would particle de Broglie wavelength be equal to the classical EM wavelength?
19. ### B Electron Diffraction and the DeBroglie Wavelength

I've been reading up on electron diffraction for electron microscopy, and I have been trying to understand the proof for the wavelength of an electron in a tunneling electron microscope. The proof I have been trying to emulate begins as follows: It then says that I must account for...
20. ### De Broglie wavelength and energy levels

Homework Statement In the earliest circular planetary model of the atom the electron and proton orbited a common centre. The electrostatic forces alone provided the force field. However an accelerating charged body will send out electromagnetic waves and the orbiting charges would consequently...
21. ### A The de Broglie wavelength: What happens in the case of a frame change?

I have a problem to understand the de Broglie wavelength. We know that also particles undergo scattering and interference at a double slit. The interference pattern is calculated by the use of the de Broglie wavelength which is defined as lambda = h / p ; p is the momentum of the particle. This...
22. ### Double-slit experiment: What is the speed of the neutrons?

Homework Statement An experiment was performed in which neutrons were shot through two slits spaced 0.10 mm apart and detected 3.5 m behind the slits. The following figure shows the detector output. Notice the 100 μm scale on the figure. To two significant figures, what was the speed of the...
23. ### I 1 pm de Broglie wavelength? What's pm?

I'm reading about delayed-choice experiments http://arxiv.org/pdf/1407.2930.pdf and in this sentence "In modern interferometric experiments, the wave nature of molecules of approximately 7000 atomic mass units and 1 pm de Broglie wavelength has been demonstrated" I can't figure out or find out...
24. ### I De Broglie wavelength - relativistic correction

According to the wiki page: http://en.wikipedia.org/wiki/Matter_wave the generalised form for the de Broglie wave is simply: \lambda = h/p I suppose this not correct, because there is no trasform which can change only one side of the equation. In this case we have two variables: 1. a momentum...
25. ### A De Broglie Wavelength - Compound Particles, Particle Systems

Can someone describe the physical processes which distinguish between separate and single particles when dealing with a collection of particles in the context of the De Broglie wavelength? The De Broglie wavelength is inversely proportional to the momentum of a "particle". Assume "separate"...
26. ### I Wave-particle duality and localization

I have read recently that the motion of an electron of momentum p must be described by the means of a plane waves :\psi(\vec r,t)=Ae^{i(\vec k \cdot \vec r -wt)}=Ae^{i(\vec p\cdot \vec r -Et)/\hbar} de Broglie hypothesis states that every particle of momentum p has a wavelength lamda. I will...
27. ### De Broglie wavelength and velocity

I was wondering about the equation for the de Broglie wavelength which indicates that the wavelength of any object is shorter when the object is moving faster. Why does this occur? And how we connect this with special relativity where the velocity depends on the frame of reference.
28. ### De Broglie Wavelength for 1Mev electron

Homework Statement Calculate the de Broglie Wavelength of a 1 MeV electron. Express your answer in femptometers. Homework Equations ## λ = h/p ## ## p = (2mT + T^2/c^2)^{1/2} ## The Attempt at a Solution basically just plugged everything in. ## λ = \frac{h}{(2mT + T^2/c^2)^{1/2}} ## ## λ...
29. ### De Broglie wavelength of a train

Homework Statement Imagine you are traveling in a train, and see in the distance how the train path splits into two parallel tracks separated by a distance d.1) Obtain an analytical expression of the de Broglie wavelength of the train. 2) What condition would you use to determine at what point...
30. ### De broglie wavelength for helium and distance between atoms

Homework Statement Consider a balloon filled with helium gas at room temperature (T = 294 K) and atmospheric pressure. Calculate (a) the average de Broglie wavelength of the helium atoms and (b) the average distance between atoms under these conditions. The average kinetic energy of an atom is...
31. ### Calculating the De Broglie Wavelength of an Accelerated Particle

Homework Statement A particle of mass m and charge q is accelerated across a potential dierence V to a non-relativistic velocity. What is the de Broglie wavelength of this particle? Homework Equations Is it The Attempt at a Solution I think it's ## \frac{h}{\sqrt{2mqV}} ##, because ##...
32. ### Show change in de Broglie wavelength from change in speed

Homework Statement Show that for a nonrelativistic particle, a small change in speed leads to a change in de Broglie wavelength given from The Attempt at a Solution I have tried to expand the left hand side of the equation, but found that it gave the answer of v0/delta v. My definition of...
33. ### De Broglie wavelength of an atom

In my book it is says, DeBroglie wavelength of a particle at temp T is, λ = h/√(2mKT) and DeBroglie wavelength of He atom is, λ = h/√(3mKT) Well, λ = h/ mv and mv2/2 = (3/2) KT and so , λ = h/√(3mKT) How to prove the first one..?? and why they are different...??
34. ### Problems with De Broglie's Wavelength

I always used the matter-wave as an explanation for why the electron does not crash into the nucleus. As a standing wave, how could it? The wave would have to increase in frequency, almost infinitely, until it was the size of a point, the nucleus, which seemed like an impossible task. However...
35. ### De Broglie wavelength of nitrogen molecules

Homework Statement According to statistical mechanics, the average kinetic energy of a particle at temperature T is 3kT/2, where k is the Boltzmann constant. What is the average de Broglie wavelength of nitrogen molecules at room temperature? Homework Equations KE = 3kt/2 = p2/2m λ = h / p...
36. ### De Broglie wavelength of an ant

An ant of mass m = 1.80×10−6 kg goes through a hole of diameter D = 5.00 mm in a window screen which has thickness L = 0.600 mm. (a) What should be the approximate wavelength and speed of the ant for it to show wave behavior as it goes through the hole? I am not sure what should the...
37. ### Calculating energy from de Broglie wavelength

Given the relationships: \lambda = \frac{h}{p} = \frac{h}{mv} and E = hf for wavelike non-relativistic matter, and v = \lambda f for a general wave, one can obtain the result: E = \frac{h^2}{m \lambda^2}. Whilst for particulate matter, we have E = \frac{1}{2}mv^2, which when combined with the...
38. ### De Broglie wavelength and ideal gas entropy derivation

When the ideal gas entropy is derived, we consider N atoms in a box of volume=Lx*Ly*Lz. Then, we make the assumption that Lx,Ly,Lz >>de Broglie wavelength of atoms. I am not sure why we need to make this assumption? Thanks!
39. ### De Broglie Wavelength at Relativistic velocity

Homework Statement A particle has charge e and masse m0. It is accelerated by a charge V to a relativistic velocity. Show that its de Broglie wavelength is: \lambda = \frac{h}{\sqrt{2m_0eV}} (1+\frac{eV}{2m_0c^2})^{-\frac{1}{2}} Homework Equations \lambda = \frac{h}{p} Conservation of...
40. ### De Broglie wavelength of a tennis ball

This is a multiple choice question. The de Broglie wavelength of a moving tennis ball is calculated as 1x10^-33. This means that the moving tennis ball A)Diffracts through a narrow slit. B)Does not behave as a particle C)Does not display wave properties D)Is traveling at the speed of light The...
41. ### De Broglie Wavelength of an electron

1. The velocity of the electron in the ground state of the hydrogen atom is 2.6 x 10^8 m/s. What is the wavelength of this electron in meters?2. De Broglie's equation: lamda = h/p p=mvThe Attempt at a Solution ... (6.626 x 10^-34) / (2.6 x 10^8 x 9.11 x 10^-31) = 2.798 x 10^-12 meters This...
42. ### De Broglie wavelength of helium atoms

Homework Statement a) In the double slit interference pattern for helium atoms, the kinetic energy of a beam of atoms is 0.020 eV. What is the de Broglie wavelength of a helium atom with this kinetic energy? b) Also, estimate the de Broglie wavelength of the atoms from the fringe spacing...
43. ### De Broglie wavelength - model for comparing photons and electrons

Hello, I'm thinking about the wavelength of a freely propagating photon vs. a freely propagating electron. For the photon, we have the classical picture of oscillating E and B fields perpendicular to the direction of propagation, and we call the wavelength of the photon, which can be...
44. ### De Broglie wavelength computable by just fixing speed of light ?

Hi, I was wondering if it is possible to compute e.g. bohr radii for a metric system whose correspondence to real units is unknown and only the speed of light is known. Let's say the only thing I know is that lightwaves travel x spaceunits in t timeunits, therefore defining the speed of...
45. ### Mechanistic explanation of de Broglie wavelength

I am not proposing a particular explanation and just in case you suspect I have something in mind, I must tell you that I don't. I was wondering if anybody here has some ideas. I understand that you may have objections to my question. One of them might be that a mechanistic model would not work...
46. ### De Broglie Wavelength Thought Problem

Homework Statement A) Find the wavelength of an Ewok that has a mass of 50kg and is Running on Edor where 'h' id 1000Js at a velocity of 0.5m/s Yes the value of h to be used is 1000. B) What would the implications of him running be?Homework Equations \lambda=\frac{h}{p}The Attempt at a...
47. ### Question regarding the de Broglie wavelength of a particle.

Homework Statement A particle with charge e and mass m_0 is accelerated by a potential V to a relativistic speed. Show that the de Broglie wavelength is: λ = h / √(2 m_0 eV ) √(1+( eV / 2 m_0 c^2 )) Homework Equations E = qV λ = h/p E = √(p^2 * c^2 + m^2 * c^4 ) p = (m_0 * v) / (1 -...
48. ### Units of the Thermal de Broglie wavelength?

1. Units of the Thermal de Broglie wavelength? 2. λ = h / (2*pi*mkT)^(.5) 3. through dimensional analysis i get S (J / kg)^.5 can you even have .5 of a unit?
49. ### De Broglie Wavelength: What Is It and How Does It Affect Us?

Before i understood that the de Broglie wavelength gets smaller as the momentum increases of an object, so my think was that because our (human body) momentum is so large that the de Broglie wavelength would be so small for there to be any effect on us, i know that we are also to large to...
50. ### De Broglie wavelength in terms of accelerated potential difference

Problem: Derive a formula expressing the de Broglie wavelength (in Å) of an electron in terms of the potential difference V (in volts) through which it is accelerated. Solution (so far): The textbook's answer is the following, \lambda=12.27[V(\frac{eV}{2m_{0}c^{2}}+1)]^{-\frac{1}{2}} I'm...