- #1
astrophysics12
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Why does a large number of identical particles randomly distributed produce a diffraction pattern same as that of a single particle?
Diffraction pattern for large number of particles
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In summary, a large number of identical particles randomly distributed will produce a diffraction pattern similar to that of a single particle due to the definition of probability and the way waves add up. However, if the particles are regularly arranged, the interference pattern of the whole array will take over and produce a finer pattern.
- #2
sophiecentaur
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A single particle cannot produce a diffraction pattern. It can only arrive at one spot. Before it arrived, there was a probability distribution of where it might arrive. With a large population of particles, the actual pattern will start to show up and it will be the same as the probability distribution. The way this happens is down to the definition of probability and it can be a bit hard to accept at first. But there is loads of experiment evidence to show that the theory is correct.
- #3
nasu
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Maybe he means diffraction (of light for example) by a solid particle. The particle is fixed (more or less).
Like in laser diffraction used to find particle size.
Like in laser diffraction used to find particle size.
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sophiecentaur
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Oh yes. That would make sense. Some questions are just too shorthand for me to get the drift.nasu said:
But I have sympathy. It's like when you go into a plumbing supplies shop and ask for that bit that goes on top of my bath tap. Blank stare from over the counter.
- #5
nasu
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Yeah, even if I ask about my bath tap will be confusing. Even more if I ask about Sophiecentaur's tap. 
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sophiecentaur
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All you'll get is a bash with my monkey wrench.
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sophiecentaur
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To return to the OP. The diffraction pattern from a single particle, when light hits it, will produce maxima and minima in various directions. (looking at all this in the far field distance) Take a large number of particles and they will all produce maxima and minima in the same directions. How will all those scattered waves add up? If the positions of the particles are random, the waves in any particular direction will add (vectorially) in a random way. Looking from a given direction, you will get a set of equal amplitude waves in random phases which will add in an uncorrelated way. The effective sum of the waves will be proportional to the (equal) amplitudes of all the individual waves; where there's a maximum for one particle, there will be a maximum sum of all of them. Where there's a minimum, there will be a minimum sum.
It only works like that if there's a random distribution. Once the particles are regularly arranged, the interference pattern of whole array will take over and give you a finer pattern, corresponding to the larger spacing of particles than their diameter.
It only works like that if there's a random distribution. Once the particles are regularly arranged, the interference pattern of whole array will take over and give you a finer pattern, corresponding to the larger spacing of particles than their diameter.
1. What is diffraction pattern for large number of particles?
The diffraction pattern for large number of particles refers to the pattern of light scattered by a large number of particles, such as atoms or molecules, when they are exposed to a beam of light. This pattern can be observed when the particles are arranged in a regular pattern, such as in a crystal.
2. How is the diffraction pattern for large number of particles formed?
The diffraction pattern for large number of particles is formed when the particles interact with the incoming light waves. The particles cause the light waves to interfere with each other, resulting in a pattern of bright and dark spots depending on the arrangement of the particles and the wavelength of the light.
3. What is the significance of studying the diffraction pattern for large number of particles?
Studying the diffraction pattern for large number of particles can provide valuable information about the structure and properties of the particles. This technique is commonly used in various fields such as crystallography, materials science, and biology to analyze the arrangement and behavior of particles at a microscopic level.
4. How does the size of the particles affect the diffraction pattern?
The size of the particles can affect the diffraction pattern in several ways. Smaller particles tend to produce more complex and detailed patterns due to their smaller size and higher surface area. On the other hand, larger particles may produce simpler and less detailed patterns.
5. Can the diffraction pattern for large number of particles be used to determine the size and shape of particles?
Yes, the diffraction pattern for large number of particles can be used to determine the size and shape of particles. By analyzing the diffraction pattern, scientists can calculate the distance between particles and the angles of the diffracted light, which can then be used to determine the size and shape of the particles.