A beam of X-rays with a wavelength Ć of 0.179nm is directed at an iron crystal whose planes have a spacing of 0.1013nm. How many diffraction peaks (each arising from a different order n) are possible?

I'm really not sure how to go about solving this. Any help is appreciated. Thank you!

Bragg’s Law

nλ =2dsinθ,
n=2dsinθ/λ.
Max n when sinθ=1 =>
n=2d/λ=2•0.1013/0.179 = 1.13.
Since n has to be integer,
n=1 =>
the maxima of the 1st order on the both sides of the central max

Thamk you for your help.

To solve this problem, we need to use Bragg's law, which relates the angle of diffraction to the wavelength of the X-rays and the spacing of the crystal planes. The formula for Bragg's law is:

nƒÜ = 2d sinθ

Where:
- n is the order of diffraction
- Ć is the wavelength of the X-rays
- d is the spacing between the crystal planes
- θ is the angle of diffraction

We can rearrange this formula to solve for n:

n = (2d sinθ) / ƒÜ

In this case, we have the wavelength of the X-rays (Ć = 0.179nm) and the spacing of the iron crystal planes (d = 0.1013nm). We want to know the number of diffraction peaks, which corresponds to the number of different values of n.

To find the number of diffraction peaks, we need to determine the range of angles (θ) for which the sinθ values lie within the range from -1 to +1. The maximum value of sinθ is 1, so we can simplify the equation further:

n = 2d / Ć

Now we can calculate n:

n = 2(0.1013nm) / 0.179nm

n ≈ 1.13

Since n must be a positive integer, the number of diffraction peaks is rounded down to the nearest whole number:

Number of diffraction peaks = floor(1.13) = 1

Therefore, there is only one diffraction peak (corresponding to n = 1) possible in this scenario.