A beam of 50eV electrons travel in the x direction towards a slit of width 6 micro metres which is parallel to the y direction. The diffraction pattern is observed on a screen 2 metres away.
Use the Heisenberg uncertainty principle to estimate the minimum uncertainty in the y-component of the electrons' momentum after passing through the slit . Use it to estimate the width of the pattern produced on the screen
The Attempt at a Solution
The first thing I did was to find out the wavelength of the electrons .
Then , I assumed the electron's vertical positions are confined within the slit , so Δy=d
This is where I got stuck .
First of all , I'm not sure what's meant by the width of the pattern . The distance between the 1st order fringes / max. order fringes ? if it's the latter , since d>>λ , the max order n I obtained was 34570 , and the width would be 3106 m , which is ridiculously large . and the HUP would be of no use at all in both cases,since all i need is the angle.
Second of all , I'm not sure what ΔyΔP is limited to . I'm still new to this and I've seen variants of the formula with different limits :h/4π, h/2π , h , h/2 .....
which makes me wonder if the limits are derived and vary from situations to situations , with h/4π being the lowest limit in theory .
Any help would be appreciated