The angle of the first order diffraction

In summary, the angle of the first order diffraction, m=1, for X-rays diffracting from a crystal with a spacing of 0.175nm between atomic planes is 69o. This is determined using Bragg's law, which states that m lambda = 2 d sin(theta). As m increases, the angle theta decreases, and higher order reflections occur at larger angles.
  • #1
cake_is_a_lie
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Homework Statement



What is the angle of the first order diffraction, m=1, when X-rays diffract from a crystal in which a spacing between atomic planes is 0,175nm? The 2nd diffraction, m=2, occurs at 45o.

Homework Equations


Δr=2dcosθm=mλ
m+1/m = cos45/cosθm , because when the m increases the θm decreases.

The Attempt at a Solution


m+1/m = cos45/cosθ1
θ1 = 69o.

What do you think? Just asking because I am not 100% sure.
 
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  • #2
Last time I checked, Bragg's law was m lambda = 2 d sin(theta)...

Higher order reflections always occur at larger Bragg angles.
 
  • #3
I my case it is cosθm. Yep, I think this should be the right answer because the angle is bigger than 45o.
 

1. What is the angle of the first order diffraction?

The angle of the first order diffraction is the angle at which the first order diffraction peak appears when a monochromatic beam of light is diffracted by a grating or other diffracting element. This angle is dependent on the wavelength of the light and the spacing of the diffracting elements.

2. How is the angle of the first order diffraction calculated?

The angle of the first order diffraction can be calculated using the grating equation: sinθ = mλ/d, where θ is the diffraction angle, m is the order of diffraction, λ is the wavelength of light, and d is the spacing between the diffracting elements.

3. What is the significance of the angle of the first order diffraction?

The angle of the first order diffraction is significant because it can be used to determine the wavelength of a light source. By measuring the angle and knowing the grating spacing, the wavelength of the light can be calculated using the grating equation.

4. How does changing the grating spacing affect the angle of the first order diffraction?

Changing the grating spacing will change the angle of the first order diffraction. As the spacing increases, the angle of diffraction decreases, and vice versa. This is because a larger spacing will result in a smaller diffraction angle for a given wavelength.

5. Can the angle of the first order diffraction be changed by altering the wavelength of the light?

Yes, the angle of the first order diffraction is directly proportional to the wavelength of the light. As the wavelength increases, the angle of diffraction also increases. This relationship is described by the grating equation, where wavelength is in the numerator.

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