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23 August, 05:39

You shoot a beam of electrons through a double slit to make an interference pattern. after noting the properties of the pattern, you then double the speed of the electrons. what effect would this have?

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  1. 23 August, 06:07
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    The distance between bright patterns y is dictated by the formula:

    y = (λ*D) / d, where λ is the de Broglie wavelength, D is the distance from the double slit to the screen and d is the spacing between the slits.

    Since de Broglie wavelength changes like:

    λ=h/p, where h is the Planck's constant and p is the momentum.

    And the momentum is p=m*v, where m is the mass of the electron and v is the velocity.

    Since we can see that λ=h/m*v so that the higher the frequency the smaller the wavelength, this is going to have an impact on the interference pattern.

    y={ (h/m*v) * D}/d = (h*D) / (d*m*v), we see that as we double the velocity v, or in other words, we put 2*v that y is going to be 2 times smaller because:

    y = (h*D) / (2*d*m*v), we have number 2 in the denominator. We can rewrite this as:

    y = (1/2) * { (h*D) / (d*m*v) }

    So the effect of doubling the speed of the electron is going to shrink the distance between the bright patterns in half.
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