Question

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?

Answer 1

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.