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A Level Physics Radioactivity - Nuclear Radius

Hi guys, this question is on the Radioactivity topic in AQA A-Level Physics

When learning about the electron diffraction, we are given the equation

sin theta(min) = 0.61(lamda)/D

I know what each of the symbols mean but could somebody please explain what the value of 0.61 represents? Any help would be appreciated,

Thanks :h:
In your equation if you take nuclear diameter D=2RD=2R then your relation looks like Dsin⁡θ=1.22λD\sin\theta=1.22\lambda

If you want to resolve two objects separated by a distance DD you can use Rayleigh criterion.

This leads to dip in the maximum diffracted intensity and first appearance of two objects takes place. Since the angle spanned by the central diffraction peak is 1.22λ/D1.22\lambda / D this means that we can't resolve objects unless the angular separation is greater than 1.22λ/D1.22\lambda / D


The intensity of diffracted light from a circular aperture is given by I(θ)=I0(2J1(x)x)2I(\theta)=I_0\Big(2\frac{J_1(x)}{x}\Big)^2

J1(x)J_1(x) is the Bessel function of order one x=kDsin⁡θx=kD\sin\theta and k=2π/λk=2\pi/\lambda

J1J_1 is a special function that turns up in in the solutions to partial differential equations depicting the scattering, especially in partial wave analysis.

http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html
(edited 7 years ago)
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titfortat
OP
12
Original post by AishaGirl
In your equation if you take nuclear diameter D=2RD=2R then your relation looks like Dsin⁡θ=1.22λD\sin\theta=1.22\lambda

If you want to resolve two objects separated by a distance DD you can use Rayleigh criterion.

This leads to dip in the maximum diffracted intensity and first appearance of two objects takes place. Since the angle spanned by the central diffraction peak is 1.22λ/D1.22\lambda / D this means that we can't resolve objects unless the angular separation is greater than 1.22λ/D1.22\lambda / D


The intensity of diffracted light from a circular aperture is given by I(θ)=I0(2J1(x)x)2I(\theta)=I_0\Big(2\frac{J_1(x)}{x}\Big)^2

J1(x)J_1(x) is the Bessel function of order one x=kDsin⁡θx=kD\sin\theta and k=2π/λk=2\pi/\lambda

J1J_1 is a special function that turns up in in the solutions to partial differential equations depicting the scattering, especially in partial wave analysis.

http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html


Ahhhh okie this is the reason why my teachers didn't want me to know :lol:

Thank you for showing me why we use it! Now I realise that for A Levels, I just need to know the value :lol:
Original post by titfortat
Ahhhh okie this is the reason why my teachers didn't want me to know :lol:

Thank you for showing me why we use it! Now I realise that for A Levels, I just need to know the value :lol:


If you need to see it explained, I have linked a video with the time.

https://youtu.be/L0q8u0N5K_Y?t=2281
Reply 4
Avatar for titfortat
titfortat
OP
12
Original post by AishaGirl
If you need to see it explained, I have linked a video with the time.

https://youtu.be/L0q8u0N5K_Y?t=2281


Thank you so much!!

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