Question

gold with atomic radius 1.44 A° and FCC structure is being used to determine wavelength at x -rays , calculate the wavelength of x-rays if the ( 1 1 1 ) plane diffracts the beam by 32° . assume first order diffraction.​

Answer 1

Answer:

Therefore the wavelength of X-rays is $220.4 \mathrm{pm}$

Explanation:

Step 1: The wavelength, which will also apply to troughs, is the separation between two wave crests. The frequency is measured in cycles per second (Hz), which is the quantity of vibrations that cross a specific area in a second (Hertz). In this article, the relationship between wavelength and frequency is covered.

Step 2: The distance between the two crests or troughs of the light wave is known as the wavelength of light. Using the Greek letter lambda(λ)., it is identified. As a result, wavelength refers to the separation between one wave's peak or dip and the following wave.

Step 3: The distance between layers in a $\mathrm{NaCl}$ crystal is $282 \mathrm{pm}$ X-rays are diffracted from these layers at angle of 23 degree assuming n=1

To find wavelength of X-rays = in $n \mathrm{~nm}$.

Bragg's Law of X-ray

Diffraction, $n \lambda=2 d \sin \theta$

$\mathrm{d}=282 \mathrm{pm}$

$0=1.44$ degree

So, $\quad 1 \times \lambda=2 \times 282 \sin 1.44$

$\lambda=220.4 \mathrm{pm}$

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