A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum py in the y-direction then for a majority of electrons passing through the slit (h is Plancks constant) :

  • Option 1)

    \left | P_{y} \right |d\simeq h

  • Option 2)

    \left | P_{y} \right |d> h

  • Option 3)

    \left | P_{y} \right |d< h

  • Option 4)

    \left | P_{y} \right |d> > h

 

Answers (1)

As we learnt in

Fraunhofer Diffraction -

b\sin \theta = n\lambda
 

- wherein

Condition of nth minima.

b= slit width

\theta = angle of deviation

 

 dsin\theta=\lambda\ \; \Rightarrow\ \;sin\theta=\frac{\lambda}{d}<1

\lambda<d\ \; \left[\lambda=\frac{h}{[P_{y}]} \right ]

\frac{h}{[P_{y}]}<d

\therefore\ \; h<|P_{y}|d

|P_{y}|d<h

Correct option is 3.

 


Option 1)

\left | P_{y} \right |d\simeq h

This is an incorrect option.

Option 2)

\left | P_{y} \right |d> h

This is an incorrect option.

Option 3)

\left | P_{y} \right |d< h

This is the correct optopn.

Option 4)

\left | P_{y} \right |d> > h

This is an incorrect option.

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