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.
