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
=
h
m
v
.
{\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.
I cannot understand why the electron orbit should be an integer multiple of De Broglie wavelength. Why should the wave path "fit" the electron orbit for it to be stationary?
Am I correct in thinking that the quantum mechanical de broglie wavelength explains relativity's contraction of matter? because lambda = h/p, as the velocity of say a proton increases, the momentum also increases, and the wavelength should get smaller because lim p-->infinity of h/p = 0. At very...
De broglie wavelength of fast moving particle--help please!
Homework Statement
A particle moving with kinetic energy equal to its rest energy has a de Broglie wavelength of 1.7898 *10^-16 m. If the kinetic energy doubles, what is the new de Broglie wavelength?
Homework Equations...
Homework Statement
A certain crystal has a set of planes 0.33 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at ∅= 38°. What is the de Broglie wavelength of the neutrons?
Homework Equations
nλ = Dsin∅ where D...
The atoms in a gas can be treated as classical particles if their de Broglie wavelength is much smaller than the average separation between the particles. Compare the average de Broglie wavelength and the average separation between the atoms in a container of monatomic helium gas at 1.00 atm...
Homework Statement
In quantum mechanics the de Broglie wavelength of an object depends
on its momentum according to λ=h/p where h is Planck's constant.
Protons of charge e and mass m are accelerated from rest through a
potential V. What is their de Broglie wavelength?
A) 2h/\sqrt{}meV...
As we know that the properties of nanoscale material are quite diffrent from the bulk's. But what's the threshold of the size, or what the upper limmit where significant difference can be observed? The De Broglie wavelength or the Fermi wavelength of the electron in material? How to understand that?
Homework Statement
What is the De Broglie wavelength of an electron with KE= 8.5 eV?
Homework Equations
λ=h/p
KE=0.5mv2
p=mv
The Attempt at a Solution
I converted 8.5 eV into joules:
8/5 eV × 1.602e-19 J = 1.3617e-18
Then used it for KE to solve for v:
I got 1729006.11...
Homework Statement
http://img580.imageshack.us/img580/7492/50177994.jpg
The Attempt at a Solution
I first attempt part (a) since both parts are similar:
(a) I need to know "v" in order to use the following equation to find the de Broglie wavelength:
\lambda = \frac{h}{p}...
We can calculate a de Broglie wavelength for a particle with momentum p. My question is does this apply to the lateral size of the particle? Perpendicular to the motion the momentum is zero. What can we say about the size of the particle in the perpendicular direction?
While deriving De-Broglie wavelength we equate mc^2 to hf and then for electron we change c to v but as far I know mc^2 is rest energy then how could c be converted into v for electron.Shouldnt it have the same rest energy?
I'm reviewing for one of my final exam and I can't seem to figure out this problem:
Find the Debroglie wavelength of an electron with a KE of 40 ev.
I got an answer of 3.9 x 10^-10 m.
I keep getting it wrong and I'm not sure what to do.
Thanks in advance!
Homework Statement
Bose-Einstein condensation of a fluid occurs when the de Broglie wavelength of a "typical" particle becomes greater than the average nearest-neighbor distance. One can interpret the momentum in the de Broglie equation as
p=\sqrt{<p^{2}>}
where <p^{2}> means the thermal...
Homework Statement
(a) Find the kinetic energy of an electron whose de Broglie wavelength is equal to 0.63 Å, a typical atomic size.
Ke = 379 eV
(b) Repeat part (a) for an electron with a wavelength equal to 1.7 x 10-15 m, a typical nuclear size.
Ke = _____eV
Homework Equations...
Homework Statement
In the Bohr model of the hydrogen atom, if the electron is in the second orbit with a radius of 2.12 Å. What is the de Broglie wavelength of the electron?
Homework Equations
λ = 4h^2ε/me^2
The Attempt at a Solution
I found this equation hunting around online and...
Find the kinetic energy of the following particles that each have a de Broglie wavelength of 0.50 nm.?
(a) photons
____eV = 2480eV
(b) electrons
____eV
(c) neutrons
____eV
(d) α particles
____eV
i know E= hc/wavelength which = a and after that I am stuck i know that the wavelength =...
Hello there,
If an object has a mass of 1 in arbitary units, and it's velocity is zero relative to you, what is the de Broglie wavelength? Shouldn't p be zero in this case? Or am I missing something related to intrinsic energy and momentum?
Thank you very much.
Homework Statement
Find the de Broglie wavelength for an electron with v=0.001c. Find the angular width of the central bright fringe in a double slit experiment, with the separation of the two slits d=50nm.
Homework Equations
wavelength = h/mv
d sin(theta)=n*wavelength
The...
Photons are blue-shifted as they accelerate in free-fall toward the earth. When an electron or positron is conceptualized as a wave using de Broglie's equation, are the de Broglie wavelengths of the electron or positron shortened (blue-shifted) as they accelerate toward the Earth in free-fall...
Question-A certain crystal has a set of planes spaced 0.376 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at a scattering angle (i.e angle between incoming neutrons and reflected beam) of 41.4 degrees. What is the de...
i was working on atomic structure and i stuck here.
how can a wave be associated to any material? is it related to wavelength of colur it emits or is it the wavelength of vibrations after it has been stuck by something?
what is it??
I had this https://www.physicsforums.com/showthread.php?p=3200140#post3200140", which I posted on PF. I got the answer, but then I started thinking more about it and have some theoretical questions.
If you did have this particle of mass m in a box of length L, which you are trying to stop...
Homework Statement
To "obeserve" small objects,one measures the diffraction of the particles whose de Broglie wavelength is approximately equal to the object's size.
Find the kinetic energy(in electron volts) required by the electrons to resolve
c) a nucleus of size 10fm.
Homework...
I have a few questions:
1. 'small smoke particles in air are seen under a low magnification microscope to move randomly at a speed of 0.10mm/s. The speed of sound in air is 330m/s. Estimate the mass of the smoke particles.
I cannot make the link between speed of particle and speed of sound -...
Homework Statement
An electron in the first Bohr orbit of a hydrogen atom (a_0=5.3*10^-11m) has a KE of 13.6 eV. Express the de Broglie wavelength for this electron in multiples of the atomic circumference.
Homework Equations
lambda=h/p
=h/(sqrt(2mqV)
The Attempt at a...
Homework Statement
What is the de Broglie wavelength of a neutron traveling with a momentum equal to 300 \frac{\text{MeV}}{\text{c}}?
Homework Equations
\lambda = \frac{h}{p}
The Attempt at a Solution
p = \frac{300 \cdot \left( \left(1\times10^6 \right) \times...
I've been studying quantum physics for a little over a semester now and I'm having trouble wrapping my head around the physical significance of matter waves. The derivation also confuses me because it states the momentum of particle with mass as mc, which is only true for a massless photon. I...
Just a random thought: is it not possible for a person to move slow enough to have an observable de Broglie wavelength? For example a person moving at around 10^-30 m/s should have a wave nature that is very observable.
Homework Statement
By estimating the De Broglie wavelength and the inter-particle spacing, find whether the following systems of particles are degenerate:
(i) a gas of neutrons in a neutron star with mass density 10^17 kg/m^3 at the temperature of 10^8K
(ii)a gas of oxygen molecules at...
Homework Statement
Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by
\lambda = \frac{hc}{\sqrt{KE(KE + 2mc^2)}}
Homework Equations
The Attempt at a Solution
I know:
KE = {\gamma}mc^2 - mc^2 = pc - mc^2
But from here I am...
Homework Statement
In his presentation of the de Broglie wavelength and the wave/particle duality, my quantum prof. has an exercise: "Find the de Broglie wavelength of a molecular vibration. Do quantum or classical laws apply?"
Homework Equations
wavelength = h/(momentum)
...
Hello,
I've always wondered about the "relativity" of the De Broglie wavelength.
The wavelength depends on the momentum of the specific thing we are observing, thus on different frames of reference(F.O.R from now on :P) we might get different answers.
I have been looking through the web to...
Homework Statement
Calculate the de Broglie wavelength of an oxygen molecule (molecular mass 32)in air at room temperture.
Homework Equations
P = h/ \lambda
P= mv
E= hv = 1/2mv^{2} = P^{2}/(2m)The Attempt at a Solution
hv = 1/2mv^{2}
h = 1/2mv
If v = P/m then h = mp/2m
so p= 2h
This...
Homework Statement
What is the de Broglie wavelength of a neutron whose kinetic energy is equal to the average kinetic energy of a gas of neutrons at temperature T = 17 K?
Homework Equations
lambda = h/p = h/mv.
The Attempt at a Solution
Well first I tried taking the h =...
Homework Statement
Earth has the mass 6 · 10^24 kg and the orbit radius r = 1.5 · 10^11 m.
(a) Compute its de Broglie wavelength. (b) Apply de Broglie quantization condition
as in the case of the Hydrogen atom and compute the quantum number n for the
orbit of Earth. (c) What is the...
Homework Statement
In an electrom microscope we wish to study paprticles of diameter about 0.10 µm (about 1000 times the size of a single atom).
What should be the de Broglie wavelength of the electrons?
Through what voltage should the electrons be accelerated to have that de Broglie...
Homework Statement
Find the de Broglie wavelength of an 8 MeV proton.
Homework Equations
y = h/p
where y is the wavelength
p = mv
K = Eo/sqrt(1-v^2/c^2)
where Eo is the rest mass and K is the kinetic energy
The Attempt at a Solution
I make the assumption that "an 8 MeV proton"...
Hi there,
Is it possible if an object were to hypothetically gain enough momentum such that its de Broglie wavelength is equivalent to, say, some light in the visible spectrum, that the object would emit light?
Thanks!
OK so you get to the matter wave equation 'lambda = h / p' using E=cp - which describes the energy for massless particles. I can understand this holding for when cp>>mc^2 , but not for when the mc^2 is comparible. Any help?
Wavelength of an electron
Homework Statement
-Electron has 3.00 MeV (or 4.8*10^-13 Joules)
-it's relativistic
-finding λ.
Homework Equations
h=6.63*10^-34
λ=h/p (obviously)
And I'm not sure if they're needed, but the relativistic eq's are:
KE = mc^2/sqrt(1-(v/c)^2)...
Homework Statement
an electron is moving at 2.5 x 105m/s. Find the electron's De Broglie Wavelength.
Homework Equations
De Broglie relates wavelength of electron waves to momentum of the electron by lambda = h/p where h is Planck's constant.
The Attempt at a Solution
given the...
Homework Statement
What was the significance of the de Broglie equation?
Homework Equations
p = h/λ
p = mv
The Attempt at a Solution
It says that not only do waves act as particles, transferring energy and momentum to matter only at localised points, but moving particles (e.g...
Homework Statement
The potential-energy function U(x) has the constant value U_0 in the interval 0 < x < L and is zero outside this interval. An electron is moving past this square barrier, but the energy of the electron is greater than the barrier height.
If E= 6 U_0, what is the ratio...
Homework Statement
In one of the classes, a recent experiment showing the interference of C60 molecules using a double slit apparatus was discussed.
(a) If the average velocity of the C60 molecules is v= 200 m/s, calculate the De Broglie wavelength for a C60 molecule
Homework Equations...