FULLSCREEN PRINTER VERSION BACK Chapter 29, Problem 38 GO Particles pass through

Question

FULLSCREEN PRINTER VERSION BACK Chapter 29, Problem 38 GO Particles pass through a single slit of width 2.2 mm (see Figure 29.15). The de Broglie wavelength of each particle is 524 nm. After the particles pass through the slit, they spread out over a range of angles. Assume that the uncertainty in the position of the particles is one-half the width of the slit, and use the Heisenberg uncertainty principle to determine the minimum range of angles. First dark fringe Midpoint of central bright fringe Single slit First dark fringe Figure 29.15 the tolerance is +/-296

Explanation / Answer

Given :

Slit width (W) = 2.2 x 10-3 m

Wave length () = 524 x 10-9 m

Minimum range of angles is :

   = tan-1 ( Py /Px )   ----------------(1)

Here   Py =   h /2 W = (6.625 x 10-34 ) / (2 x 3.14 x 2.2 x 10-3 m ) = 4.79 x 10-32

Px   = h /    =   (6.625 * 10-34 ) / 524 x 10-9 = 1.26 x 10-27

Hence eqn (1) becomes ,

    =    tan-1 (4.79 x 10-32 / 1.26 x 10-27  ) = 2.17 x 10-3 degree

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