Question

An electron microscope produces electrons with a $2.00-\mathrm{p}\mathrm{m}$ wavelength. If these are passed through a $1.00-\mathrm{n}\mathrm{m}$ single slit, at what angle will the first diffraction minimum be found?

Short answer

The first minimum can be found at an angle that equals$0.115^{{}^{\circ }}$.

Step-by-step solution

Definition of diffraction

Diffraction is a term that describes a variety of events that occur when a wave collides with an obstruction or a slit. The bending of waves around the corners of an obstruction or aperture into the geometrical shadow of the barrier is specified.

Find the angle of diffraction

Consider the equation to determine the diffraction:

$D\sin \left(\theta \right)=m\lambda$

Here, $m=1$.

Determine the value for $\theta$

$\begin{array}{rl}\theta & ={\sin }^{-1}\left(\frac{m\lambda }{D}\right)\\ & ={\sin }^{-1}\left(\frac{1\times 2.00\times {10}^{-12}m}{1.00\times {10}^{-9}m}\right)\\ & ={0.115}^{\circ }\end{array}$

Therefore, the first minimum can be found at an angle that equals $0{.115}^{\circ }$.