De Broglie Hypothesis | De Broglie Wavelength
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- เผยแพร่เมื่อ 4 ต.ค. 2024
- De Broglie Hypothesis and De Broglie Wavelength
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The de Broglie hypothesis is a concept in quantum mechanics proposed by Louis de Broglie in 1924. It suggests that particles, such as electrons, exhibit both particle-like and wave-like properties. According to de Broglie, particles like electrons can have associated wavelengths, similar to how waves are described in classical physics.
The de Broglie wavelength (λ) is given by the de Broglie equation:
λ = h / p
where λ is the de Broglie wavelength,
h is Planck's constant 6.626 x 10^-34
p is the momentum of the particle.
This equation implies that particles with larger momentum (mass times velocity) have shorter de Broglie wavelengths, and particles with smaller momentum have longer de Broglie wavelengths. The de Broglie wavelength is a fundamental concept in quantum mechanics and is particularly significant in understanding phenomena like wave-particle duality and the behavior of particles at the quantum level.
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λ = h / p
where h is Planck's constant.
Since kinetic energy (KE) is related to momentum by:
KE = p^2 / (2m)
where m is the mass of the electron, we can express the change in kinetic energy as:
ΔKE = (p2^2 - p1^2) / (2m)
Given that the kinetic energy increases by 96%, we can write:
ΔKE = 0.96KE1
where KE1 is the initial kinetic energy.
Substituting the expression for KE in terms of momentum, we get:
(p2^2 - p1^2) / (2m) = 0.96(p1^2 / (2m))
Simplifying, we get:
p2^2 = 1.96p1^2
Taking the square root of both sides:
p2 = √1.96p1 ≈ 1.4p1
Now, using the de Broglie equation, we can find the change in wavelength:
λ2 = h / p2
= h / (1.4p1)
≈ 0.71λ1
So, the wavelength decreases by about 29% (1 - 0.71 ≈ 0.29).
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I guess you don't know the dot of quantum. Sir ki video toh khud sur confuse lag raha hae. Theory is not physics it's understanding.
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Thanks 🙏 from Bangladesh 🇧🇩. Does that means that all object r high Frequency least wavelength? 2. All objects r frozen light?
5.0127×10^-19
It's energy that was thought to be continuous, not matter.
Good 👍
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Physics Father
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Are number of electrons reduced when metal was exposed to light ?
It was a very helpful video. Love from Bangladesh. ❤
Let's dive deeper into the concept of "systems" and their role in the context of de Broglie wavelengths and quantum mechanics.
What is a system in physics?
In physics, a system is simply a collection of objects or entities that we choose to focus our attention on. It's a way of mentally separating a part of the universe from the rest, so we can analyze its behavior and interactions more easily.
Types of Systems
* Isolated System: No exchange of matter or energy with its surroundings. A perfectly isolated system is an idealization, but some systems come close (e.g., a well-insulated thermos).
* Closed System: Can exchange energy but not matter with its surroundings (e.g., a sealed container with a hot liquid).
* Open System: Can exchange both matter and energy with its surroundings (e.g., a living organism).
Why Systems Matter in Quantum Mechanics
When we talk about a particle's de Broglie wavelength interacting with a system, we're essentially talking about how the particle's wave function interacts with the potential energy landscape or boundaries defined by that system.
* Confinement: Systems can confine particles to specific regions of space, altering their wave functions and energy levels. This leads to phenomena like quantum confinement in nanostructures, where the particle's behavior is strongly influenced by the system's boundaries.
* Scattering and Diffraction: When a particle interacts with a system, its wave function can be scattered or diffracted, revealing information about the system's structure. This is the basis for techniques like electron microscopy and neutron scattering.
* Tunneling: In quantum mechanics, particles can "tunnel" through potential energy barriers, even if they don't have enough classical energy to do so. The probability of tunneling depends on the particle's de Broglie wavelength and the shape of the barrier, which is often determined by the system's properties.
Choosing the Right System
The choice of system depends on the specific problem or phenomenon we're interested in.
* Single Particle in a Potential: We might consider a single particle (e.g., an electron) interacting with a potential well or barrier created by some external field or structure. This allows us to focus on the particle's wave function and energy levels within that specific environment.
* Many-Particle Systems: In more complex systems, we need to consider the interactions between multiple particles, which can lead to collective phenomena like Bose-Einstein condensation or superconductivity.
* Open Systems: In some cases, we need to account for the exchange of matter and energy with the surroundings, which can lead to decoherence and other effects that influence the quantum behavior of the system.
Key Takeaway
The concept of a "system" provides a framework for analyzing the behavior of particles in quantum mechanics. By defining the system and its boundaries, we can understand how a particle's de Broglie wavelength interacts with its environment, leading to a wide range of quantum phenomena.
Let me know if you'd like to explore any specific examples or aspects of systems in more detail. I'm here to help!
the wavelength decreases by about 29% (1 - 0.71 ≈ 0.29).
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If we let the first kenetic energy is KE1 and The second kenetic energy is KE2 then the answer will be -0.2hKE1m
h =Planck's constant
m=the mass of an electron
KE1=the first kenetic energy
I hope you will give me a correction if I'm wrong 🙏
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the percentage change in wavelength is 2.14%.
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28.57% dicreases
how to find
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what is the answer for the question? please help ?
7/5
0.13383×10-34
The fact that the energy levels are quantized doesn’t mean that there are particles. Rather, it is all waves but “quantized waves” as I call them. They give the false impression of particles but do account for the so called “dual nature of particles”.
Change in wavelength=2/5 and %change in wavelength= 40%
Sir from which website you use simulations like you use photoelectric effect in this video ??
Wavelength will decrease by 28.5 %
Sir please pin if ans is correct ❤
Sir is the change in wavelength 92.8%
27%
Amazing🎉
The answer is:
1.4 times the initial wavelength.
i.e.,
Final wavelength=1.4 initial wavelength
or,
λ'=1.4λ.
Hope it's true.
Please let me know.
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I got 51%....i.e the wavelength decreases by 51%
Thank you.... your explanation is crystal clear
0.287 decrease
Sir please Give tha answer of last Question
Is this KEf=kei+96%(ke) i
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98% decrease
71.428% increase in wave length.
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First
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Decrease 28.571428571 %