The wavelength of these 'material waves' - also known as the de Broglie wavelength - can be calculated from Planks constant h divided by the momentum p of the particle.
What is the de Broglie wave formula?
de Broglie derived the above relationship as follows: 1) E = hν for a photon and λν = c for an electromagnetic wave. 2) E = mc 2, means λ = h/mc, which is equivalent to λ = h/p. Note: m is the relativistic mass, and not the rest mass; since the rest mass of a photon is zero.
What is the DeBroglie wavelength of a human being?
1.2: Atomic Spectroscopy and the deBroglie Wavelength
- Distinguish between line and continuous emission spectra
- Describe the particle nature of light
- Extend the concept of wave–particle duality that was observed in electromagnetic radiation to matter as well
- Calculate deBroglie wavelengths
What is the velocity of the de Broglie wave?
De Broglie’s hypothesis of matter waves postulates that any particle of matter that has linear momentum is also a wave. The wavelength of a matter wave associated with a particle is inversely proportional to the magnitude of the particle’s linear momentum. The speed of the matter wave is the speed of the particle.
How do you find the wavelength using binding energy?
Problems & Exercises
- 2 H is a loosely bound isotope of hydrogen. ...
- 56 Fe is among the most tightly bound of all nuclides. ...
- 209 Bi is the heaviest stable nuclide, and its BE/ A is low compared with medium-mass nuclides. ...
- (a) Calculate BE/ A for 235 U, the rarer of the two most common uranium isotopes. ...
- (a) Calculate BE/ A for 12 C. ...
What is de Broglie formula?
The de Broglie equation is an equation used to describe the wave properties of matter, specifically, the wave nature of the electron: λ = h/mv, where λ is wavelength, h is Planck's constant, m is the mass of a particle, moving at a velocity v. de Broglie suggested that particles can exhibit properties of waves.
What is the de Broglie wavelength of the wave?
de Broglie wavelength is an important concept while studying quantum mechanics. The wavelength (λ) that is associated with an object in relation to its momentum and mass is known as de Broglie wavelength. A particle's de Broglie wavelength is usually inversely proportional to its force.
How do you find the de Broglie wavelength with voltage?
1 AnswerThe de Broglie wavelength λ=1.23 x 10−9m .So if a charge of e coulombs is moved through a potential difference of V volts then the work done is eV Joules.In this case e is the charge on the electron which is equal to. ... The mass of the electron m=9.11 x 10−31kg.From which v=5.9 x 107m. ... 6.63 x 10−34J.More items...•
How do you calculate the wavelength of a matter wave?
The relationship between momentum and wavelength for matter waves is given by p = h/λ, and the relationship energy and frequency is E = hf. The wavelength λ = h/p is called the de Broglie wavelength, and the relations λ = h/p and f = E/h are called the de Broglie relations.
How can wavelength be calculated?
How do you measure wavelength?Use a photometer to measure the energy of a wave.Convert the energy into joules (J).Divide the energy by Planck's constant, 6.626 x 10-34, to get the frequency of the wave.Divide the speed of light, ~300,000,000 m/s, by the frequency to get wavelength.
What is de Broglie wavelength for an electron with velocity of light?
The de Broglie wavelength of an electron moving with a velocity c/2 (c=velocity of light in vacuum) is equal to the wavelength of a photon.
What is the de Broglie wavelength of an electron at 100 EV?
=1.23 × 10−10 m = 1. 23Ao.
What determines the value of de Broglie wavelength of an electron?
The velocity of the electron determines the de Broglie wavelength of the electron.
How to Calculate the de Broglie Wavelength of a Particle
Step 1: Determine the momentum of the object, either given or calculated from the mass and the velocity of the object.
What is the de Broglie Wavelength?
De Broglie Wavelength: De Broglie wavelength is a principle that even massive objects have a probability density. This probability density is determined by a wavelength, in this case, the de Broglie wavelength, made famous by the French physicist de Broglie. It is calculated from Planck's constant divided by the momentum of the object.
Example in How to Calculate the de Broglie Wavelength of a Particle with a Known Momentum
A ball is moving with a momentum of {eq}1000\ \mathrm {kg m/s} {/eq}. What is the de Broglie wavelength of the ball?
Example on How to Calculate the de Broglie Wavelength of a Particle with Known Mass and Velocity
A car has a mass of 1,200 kilograms and is traveling at 30 meters per second. What is the de Broglie wavelength of the car?
Calculating the de Broglie Wavelength of an Electron
Step 1: Read the question carefully and determine what is being asked.
Calculating the de Broglie Wavelength of an Electron Equations and Vocabulary
In this equation, {eq}\lambda {/eq} is the "de Broglie Wavelength" of a particle, m represents the mass of the particle, and v is its velocity. In this equation, h is "Planck's constant." The value for Planck's constant, and the mass of an electron, are given below:
Calculating the de Broglie Wavelength of an Electron Example: Calculating Wavelength
An electron leaves an atom traveling at a velocity of 120 m/s. What is the de Broglie wavelength of the electron?
Calculating the de Broglie Wavelength of an Electron Example: Calculating Velocity
For a certain diffraction experiment, a chemist needs electrons with a de Broglie wavelength of at least 0.01 m. What velocity should the electrons have in order to have a wavelength of 0.01 m?
What is the de Broglie wavelength formula?
De Broglie Wavelength Formula. In some situations, light behaves like a wave, while in others, it behaves like particles. The particles of light are called photons, and they can be thought of as both waves and particles. Louis de Broglie (1892-1987) developed a formula to relate this dual wave and particle behavior.
Who developed the formula for the wave and particle behavior?
Louis de Broglie (1892-1987) developed a formula to relate this dual wave and particle behavior. It can also be applied to other particles, like electrons and protons. The formula relates the wavelength to the momentum of a wave/particle.
What is the wavelength of a scintillator?
Most scintillators that are used to build detectors produce light in the blue and green regions of the electromagnetic spectrum, with mean wavelengths of 475 and 510 nm, respectively.
How is the wavelength of an electron related to the momentum of the electron?
For electrons to probe the inner structure of nuclei, the wavelength of the incident electrons must be comparable to the size of the nucleus. Example 14.1.
What are the ideas of constructive and destructive interference that have enabled us to derive Bragg's law?
The ideas of constructive and destructive interference that have enabled us to derive Bragg’s law depend upon the wave model of electromagnetic radiation. One of the remarkable discoveries of modern physics is that the wave model can also be used to describe the movements of particles such as electrons. This idea, which was originally suggested by de Broglie in 1923, provides a basis for wave mechanics which plays a fundamental role in our understanding of microscopic systems. Prior to de Broglie’s work, Einstein had put forward his theory of the photoelectric effect and Bohr had proposed his model of the atom. These theories, each of which depended upon the idea that electromagnetic radiation consists of photons, were the subject of intense debate at the time de Broglie made his suggestion. He argued that just as light has both a wave and a particle character, the objects which we think of as particles should also display this wave-particle dualism. Radiation and matter should be thought of as being at once both particles and waves.
What I did
I tried to use the formula λ = h / p ( p is the momentum). I calculated p as follows: p = − i ℏ d ψ d t = − i ℏ k cos ( k x − ω t) ⟹ λ = h / p = ( 2 π k) ( i cos ( k x − ω t))
Problem
Where is the extra ( i / cos ( k x − ω t)) factor coming from? Isn’t the de Broglie wavelength just 2 π / k ?
Derivation of de Broglie’s Wavelength
De-Broglie Wavelength and Potential
- When a charged particle, having a charge \(\text {q}\) is accelerated through an external potential difference \(\text {V}\), the energy of the particle can be given as: \({\text{E}} = {\text{qV}} \cdots ({\text{i}})\) According to Planck’s equation, \(\text {E}=\text {hf}\) Since, \({\rm{f}} = \frac{{\rm{v}}}{\lambda }\) Therefore, \({\rm{E}} = {\rm{h}}\frac{{\rm{v}}}{\lambda }\,\,\, \ldots ({\…
Thermal de Broglie Wavelength
- There exists a relation between the De-Broglie equation and the temperature of the given gas molecules, and the thermal de Broglie wavelength gives it \(\left( {{\lambda _{{\rm{Th}}}}} \right).\) The Thermal de Broglie equation represents the average value of the de Broglie wavelength of the gas particles at the specified temperature in an ideal gas. The expression give…
de Broglie Wavelength of Day-To-Day Objects
- According to the hypothesis, all particles have a wave associated with them. That is true for us humans and the objects around us. To get an idea of the de-Broglie wavelength associated with macroscopic particles: Let us find the wavelength of a wave associated with a car of mass \(1000 \mathrm{~kg}\) moving with the velocity of \(10 \mathrm{~m} / \mathrm{s}.\) The wavelength …
De-Broglie Wavelength of An Electron
- As we have seen above, the matter waves associated with real objects is so small that it is of no good use to us. But for sub-atomic particles with negligible masses, the value of de-Broglie wavelength is substantial. To calculate the de-Broglie wavelength associated with a microscopic particle, Let us take an electron of mass \({\rm{m}} = 9.1 \times {10^{ – 31}}\;{\rm{kg}},\) movin…
de Broglie Wavelength- Solved Problems
- Q.1. A certain photon has a momentum of \(1.50 \times 10^{-27} \mathrm{~kg} \mathrm{~m} / \mathrm{s}\). What will be the photon’s de Broglie wavelength? Ans:\(\text {p}=1.50 \times 10^{-27} \mathrm{~kg} \mathrm{~m} / \mathrm{s}\) Plank’s constant, \(\text {h}=6.62607 \times 10^{-34} \mathrm{Js}\) The de Broglie wavelength of the photon can be computed using the formula…
Frequently Asked Questions on de Broglie Wavelength Formula
- The most commonly asked questions on De Broglie Wavelength Formula are answered here: We hope this detailed article on De Broglie Wavelength Formula helps you in your preparation. If you get stuck do let us know in the comments section below and we will get back to you at the earliest.