Bragg Law and Effect of Doubling Wavelength

In summary, the lecturer discussed Bragg's Law and explained how the angle theta changes when the wavelength is doubled. The Bragg condition for a maxima would be reduced to dsinθ=mλ when the wavelength is doubled. To predict the angles at which the maximas would now be observed, one can calculate sinθ using the given values of m and d. However, if sinθ is larger than 1, there may only be one maxima at 44.5 degrees.
  • #1
elemis
163
1
My lecturer discussed bragg's law a few weeks ago and described how the angle theta changes as the wavelength is doubled.

I can't seem to duplicate his result.

I know that the bragg condition for a maxima would reduce to : dsinθ=mλ when the wavelength is doubled.

In his example he knew that maxima were observed at 20.5 and 44.5 degrees but he gave no other values.

How would I go about predicting the angles at which the maximas are now observed ?
 
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  • #2
If you double λ and m and d stay constant, sinθ doubles as well. You can calculate sinθ in your example.
 
  • #3
mfb said:
If you double λ and m and d stay constant, sinθ doubles as well. You can calculate sinθ in your example.

True, so sin(20.5) = 0.3502... This multiplied by 2 gives : 0.700... Sin inverse of this gives 44.5 degrees.

But if I double sin(44.5) I get a value larger than 1. How is it possible to take the sine inverse of this ?

EDIT : Does this imply there is only one maxima now at 44.5 degrees ?
 
  • #4
elemis said:
EDIT : Does this imply there is only one maxima now at 44.5 degrees ?
The 44.5-maximum has no equivalent for the doubled wavelength, right.
 
  • #5


First of all, it is important to note that the Bragg Law is a fundamental principle in X-ray crystallography, which describes the relationship between the angle of incidence, the spacing of atomic planes in a crystal, and the wavelength of X-rays. It is given by the equation dsinθ = mλ, where d is the spacing of atomic planes, θ is the angle of incidence, m is the order of the diffraction peak, and λ is the wavelength of X-rays.

Now, to address your specific concern about the effect of doubling the wavelength on the angle of diffraction, we can use the Bragg Law to predict the angles at which the maxima will be observed. As you correctly stated, when the wavelength is doubled, the Bragg condition for a maximum would reduce to dsinθ = m(2λ). This means that the angle of diffraction, θ, would also change. To predict the new angles, we can use the inverse sine function (sin^-1) on both sides of the equation to solve for θ. This would give us the equation θ = sin^-1 (m(2λ)/d).

In order to determine the specific angles at which the maxima will be observed, we would need to know the values of d and m for the particular crystal that is being studied. These values can be determined experimentally or can be calculated based on the crystal structure. Once we have these values, we can plug them into the equation and calculate the new angles at which the maxima will be observed when the wavelength is doubled.

In conclusion, the Bragg Law is a powerful tool that allows us to predict the angles at which diffraction peaks will occur in X-ray crystallography. By understanding the relationship between the angle of incidence, crystal spacing, and wavelength of X-rays, we can accurately predict the changes in the diffraction pattern when the wavelength is doubled. I would recommend consulting with your lecturer or a textbook for specific examples and further clarification on the subject.
 

What is the Bragg Law?

The Bragg Law is a fundamental principle in X-ray crystallography that explains the relationship between the diffraction angles of X-rays and the spacing of atoms in a crystal lattice. It states that when an X-ray beam is incident on a crystal at a specific angle, the X-rays will diffract and produce bright spots on a detector. The spacing between these bright spots is directly related to the spacing of atoms in the crystal lattice.

How does the Bragg Law explain the diffraction of X-rays?

The Bragg Law explains that when X-rays are incident on a crystal at a certain angle, they will interact with the atoms in the crystal and diffract. This diffraction results in constructive interference between the X-rays, producing bright spots on a detector. The spacing between these bright spots is determined by the wavelength of the X-rays and the spacing of atoms in the crystal lattice, as described by the Bragg Law.

What is the effect of doubling the wavelength of X-rays on diffraction?

According to the Bragg Law, doubling the wavelength of X-rays will result in a decrease in the spacing between the bright spots on the detector. This is because the spacing between the atoms in the crystal lattice remains the same, but the longer wavelength of the X-rays will cause the angle of diffraction to decrease. As a result, the bright spots will be closer together on the detector.

Why is the Bragg Law important in X-ray crystallography?

The Bragg Law is essential in X-ray crystallography because it allows scientists to determine the atomic structure of crystals. By analyzing the angles and spacing of the diffraction spots on a detector, scientists can calculate the arrangement of atoms in a crystal lattice. This information is crucial in understanding the properties and behavior of various materials.

How is the Bragg Law used in other fields of science?

The Bragg Law has applications beyond X-ray crystallography and is used in various fields of science, such as materials science, biology, and chemistry. For example, it is used to study the structure of proteins, determine the composition of materials, and analyze the crystal structure of minerals. The Bragg Law is a fundamental principle that has revolutionized our understanding of the atomic world and continues to have significant impacts in scientific research and technology.

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