[Micky76]

Question:

Describe and explain the effect on the electron diffraction pattern if the incident electrons have smaller velocity.

Answer:
Rings spread out more [1]
de Broglie wavelength increased [1]
Diffraction increases with wavelength [1]

I understand why the wavelength is increased. My question is why does diffraction increase with wavelength? Initially, on the past paper I wrote that it will decrease since I was thinking of wave fronts approaching a slit and being diffracted with the gap being comparable. Then I thought of the equation from young's double slit which verifies the answer.

λ = ay/d
λ is proportional to y, the fringe separation.

From that I understand the answer but I can't quite grasp it when I picture the wave fronts and the slit. Could anyone explain?

[Zishi]

(Original post by Micky76)
Question:

Describe and explain the effect on the electron diffraction pattern if the incident electrons have smaller velocity.

Answer:
Rings spread out more [1]
de Broglie wavelength increased [1]
Diffraction increases with wavelength [1]

I understand why the wavelength is increased. My question is why does diffraction increase with wavelength? Initially, on the past paper I wrote that it will decrease since I was thinking of wave fronts approaching a slit and being diffracted with the gap being comparable. Then I thought of the equation from young's double slit which verifies the answer.

λ = ay/d
λ is proportional to y, the fringe separation.

From that I understand the answer but I can't quite grasp it when I picture the wave fronts and the slit. Could anyone explain?

The equation which are you using is for interference. For electron diffraction, we use . As you may see from here, increasing the wavelength increases the angle , which also means that electrons are more diffracted.

[Micky76]

(Original post by Zishi)
The equation which are you using is for interference. For electron diffraction, we use . As you may see from here, increasing the wavelength increases the angle , which also means that electrons are more diffracted.

Oops, I completely forgot about that equation even though its not on our spec. I do understand now, thank you.

[Micky76]

(Original post by Zishi)
The equation which are you using is for interference. For electron diffraction, we use . As you may see from here, increasing the wavelength increases the angle , which also means that electrons are more diffracted.

Just one last thing, the equation you wrote, its called the Bragg equation right? The problem is that I have seen it in several forms, ie:

λ = 2d sinθ
nλ = 2d sinθ
nλ = d sinθ

I see that your suggestion is for n=1. This tells me that the second equation is correct. Is the third one then, incorrect or does it simply use half the triangle used for the first two?

[Zishi]

(Original post by Micky76)
Just one last thing, the equation you wrote, its called the Bragg equation right? The problem is that I have seen it in several forms, ie:

λ = 2d sinθ
nλ = 2d sinθ
nλ = d sinθ

I see that your suggestion is for n=1. This tells me that the second equation is correct. Is the third one then, incorrect or does it simply use half the triangle used for the first two?

Sorry, my exam board just wanted me to learn the equation I told you, without telling anything other about it. So I can't comment on it.