Hey there! Sign in to join this conversationNew here? Join for free

A Level Physics Radioactivity - Nuclear Radius Watch

    • Thread Starter
    Offline

    10
    ReputationRep:
    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
    Offline

    2
    ReputationRep:
    In your equation if you take nuclear diameter D=2R then your relation looks like D\sin\theta=1.22\lambda

    If you want to resolve two objects separated by a distance D 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 1.22\lambda / D this means that we can't resolve objects unless the angular separation is greater than 1.22\lambda / D


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

    J_1(x) is the Bessel function of order one x=kD\sin\theta and k=2\pi/\lambda

    J_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/BesselF...FirstKind.html
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by AishaGirl)
    In your equation if you take nuclear diameter D=2R then your relation looks like D\sin\theta=1.22\lambda

    If you want to resolve two objects separated by a distance D 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 1.22\lambda / D this means that we can't resolve objects unless the angular separation is greater than 1.22\lambda / D


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

    J_1(x) is the Bessel function of order one x=kD\sin\theta and k=2\pi/\lambda

    J_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/BesselF...FirstKind.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:
    Offline

    2
    ReputationRep:
    (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
    • Thread Starter
    Offline

    10
    ReputationRep:
    (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!!
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.