Question

Could an electron-diffraction experiment be carried out using three or four slits? Using a grating with many slits? What sort of results would you expect with a grating? Would the uncertainty principle be violated? Explain.

Short answer

It is possible to carry out electron-diffraction using three or four slits and using grating with many slits and the uncertainty principle would still be valid.

Step-by-step solution

Given Data

Diffraction is a process by which a beam of light spreads when passing through a

narrow passage or across the edge of an obstacle accompanied by interference

between the waveforms.

Diffraction gratings are used in laboratory to disperse light into its component

wavelengths. It has many slits, which produces a very sharp maxima due to

which angle of deviation can be measured precisely.

According to Heisenberg’s Uncertainty Principle, it is impossible to simultaneously determine both the position and the momentum of a particle with great precision. Instead, uncertainties in the two quantities play complementary roles. It can be represented by the equation:

$\mathbf{\Delta y}\mathbf{\cdot }{\mathbf{\Delta p}}_{\mathbf{y}}\mathbf{~}\frac{\mathbf{\hslash }}{\mathbf{2}}$

Explanation

It is possible to carry out electron-diffraction using three or four slits and using grating with many slits. If grating is used then interference is accompanied with the diffraction. The results fit well with the wave description of the electron. Along with that, uncertainty holds true. Some important results can be deduced by passing a electron beam through a narrow opening of size that will result in an associated y-component of momentum uncertainty $∆p_y$as displayed in the picture below.