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Bragg's law states that for constructive interference of X-rays diffracted by a crystal lattice, the path difference between the waves should be equal to the wavelength \lambda.Which of the following statements is true regarding the Bragg's equation for a crystal lattice?

 

Option: 1

Bragg's equation relates the interplanar spacing d, the angle of incidence \theta, and the wavelength \lambda of the X-rays as 2d sin\theta = n\lambda,where n is an integer


Option: 2

Bragg's equation relates the interatomic distance a, the angle of incidence \theta, and the wavelength \lambda of the X-rays as a \: sin\theta = n\lambda, where n is an integer.


Option: 3

Bragg's equation relates the interplanar spacing d, the angle of incidence  \theta,and the wavelength  \lambda of the X-rays as d \: sin\theta = n\lambda,where n is an even integer.

 


Option: 4

Bragg's equation relates the interatomic distance a, the angle of incidence \theta, and the wavelength \lambda of the X-rays a 2\: d sin\theta = n\lambda,where n is an integer.

 


Answers (1)

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The Bragg's equation is a fundamental equation in crystallography that relates the diffraction angle, the interatomic or interplanar distance, and the wavelength of the incident X-rays. According to Bragg's law, when the path difference between the X-rays diffracted by a crystal lattice is equal to the wavelength \lambda the waves will interfere constructively, resulting in diffraction peaks. The Bragg's equation can be written as 2\: d sin\theta = n\lambda, where d is the interplanar spacing, \theta is the angle of incidence,\lambda is the wavelength of the X-rays, and n is an integer known as the order of the diffraction peak. Therefore, option a is the correct statement. Option b is incorrect because it refers to the interatomic distance instead of the interplanar spacing. Option c is incorrect because it implies that n must be even, which is not true. Finally, option d is incorrect because it refers to the interatomic distance and the factor of 2 is incorrect.

 

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Ritika Jonwal

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