A parallel beam of electrons travelling in x- | vedclass

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(C) According to the Heisenberg Uncertainty Principle,the uncertainty in the position of the electron in the $y-$ direction is $\Delta y \simeq d$. Th

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$|P_y|d \simeq h$

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(C) According to the Heisenberg Uncertainty Principle,the uncertainty in the position of the electron in the $y-$ direction is $\Delta y \simeq d$. The uncertainty in the momentum in the $y-$ direction is $\Delta P_y \simeq |P_y|$. From the uncertainty principle,we have $\Delta y \cdot \Delta P_y \simeq h$. Substituting the values,we get $d \cdot |P_y| \simeq h$. For the majority of electrons,the momentum acquired is of the order of the uncertainty,thus $|P_y|d \simeq h$.

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

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