Bragg's law and double-slit experiment

In summary, the conversation is discussing the construction of a double-slit experiment for 5eV electrons. The first minimum of the diffraction pattern needs to occur at 5 degrees and the separation of the slits needs to be determined. The use of Bragg's law is mentioned, but there is uncertainty about calculating minimums. Additionally, the distance between the slits and the detector plane is discussed, with reference to the interference and multiple slits. The conversation concludes by stating that a minimum should occur approximately halfway between two adjacent maxima.
  • #1
UrbanXrisis
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I am asked to construct a double-slit experiment for 5eV electrons. The first minimum of the diffraction pattern needs to occur at 5 degrees, what must the separation of slits be?

I'm guessing that I should use Bragg's law but I don't know how to calcualte a minumum because bragg's law is for maximums.

[tex]\lambda=\frac{1240eVnm}{5eV}[/tex]

[tex]n \lambda=2dsin \theta[/tex]

[tex]1x240nm=2dsin5[/tex]

i would solve for d but wouldn't that be a maximum?

Also, I am asked to determin how far the slits have to be from the detector plan if the first minima on each side of the central maximum are separated by 1 cm.

we know that theta is 5 and the height is 1 cm, so... using 1cm/theta(5)=11.4 cm? that doesn't seem right to me.

any ideas as to what i am doing wrong?
 
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  • #2
Some references on interference and multiple slits.

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslidi.html#c2

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html

The maxima occur where the difference in distance is an integral multiple of wavelength, so that two peaks constructively interact. The minima occur where a peak and trough occur, or one wave is a half-wavelength out of phase with the other, so that they destructively interfere.

So a minimum should occur approximately halfway between two adjacent maxima.
 

1. What is Bragg's law and how does it relate to the double-slit experiment?

Bragg's law is a fundamental principle in the field of X-ray crystallography that explains the diffraction pattern produced when X-rays are directed at a crystal. It states that the path difference between two waves reflected from different planes of the crystal lattice will result in constructive interference if the path difference is equal to an integer multiple of the wavelength of the X-rays. This principle is also applicable to the double-slit experiment, where the path difference between the waves passing through the two slits determines the interference pattern observed on a screen.

2. How do the parameters in Bragg's law affect the diffraction pattern in the double-slit experiment?

The parameters in Bragg's law, namely the wavelength of the incident X-rays and the angle of incidence, determine the spacing between the planes of the crystal lattice that will produce constructive interference. In the double-slit experiment, these parameters also affect the spacing between the two slits and the angle at which the waves pass through them, ultimately determining the interference pattern observed on the screen.

3. Is Bragg's law only applicable to X-rays or can it be applied to other types of waves?

Bragg's law is a general principle that can be applied to any type of wave, as long as the wavelength of the waves is comparable to the spacing between the planes of the crystal lattice. In addition to X-rays, it has also been applied to other types of waves such as electrons, neutrons, and even sound waves.

4. How does the double-slit experiment provide evidence for the wave-like nature of particles?

The double-slit experiment demonstrates the phenomenon of interference, which is a characteristic of waves. This experiment shows that when particles, such as electrons, are fired at two slits, they produce an interference pattern on the screen that is typical of waves. This supports the idea that particles also have a wave-like nature, and can exhibit behaviors such as diffraction and interference.

5. Can Bragg's law and the double-slit experiment be used to determine the properties of unknown materials?

Yes, Bragg's law and the double-slit experiment are commonly used in X-ray crystallography to determine the atomic and molecular structure of unknown materials. By analyzing the diffraction pattern produced by X-rays directed at a crystal, scientists can determine the spacing between the planes of the crystal lattice and use this information to identify the material and its properties.

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