# A beam consisting of 50 eV electrons (electron mas...

A beam consisting of 50 eV electrons (electron mass 9.11 *10^-31 kg) is incident on a thin wafer of a crystal with layerspacing 4.6 Angstroms. Surprisingly we find that theelectrons, which are particles, are scattered in such a way as toform an interference pattern identical to that of a wave. What will be the distance between central interference maxima at adistance of 18 cm from the wafer?

1. x.x?=sp;

ANS)
THE ENERGY OF 50EV ELECTRON BEAM IN JOULES IS

=   50 * 1.6 *10^-19 J

= 80 *10^-19 J

AS THE ELECTRON BEAM HAS WAVE NATURE THE WAVE LENGTH
OF THE MATTER WAVE CAN BE DETERMINED BY THE DEBROGLE RELATION
? = h/(? 2 m E)
h= planks constant
m= rest mass of the electron
E = energy of the electron beam
? = wavelength.

?   = 6.626 * 10 ^ -34 / ? (2 * 9.1 *10 ^ -31 * 80 * 10^ -19 )

= 1.7355 * 10 ^-10 m

considering this wave lenght of the electron beam falling on double slit using the
relation

X = n ? D / 2 d               ------ EQ - 1

X   IS DISTANCE OF THE MAXIMA
FROM THE MEAN POSITION    ?

n IS THE ORDER OF THE MAXIMA 1

D IS THE DISTANCE OF THE SCREEN FROM
THE WRAFER OF THE CRISTAL  18 c m

2d DISTANCE BETWEEN LAYERS OF CRYSTAL 4.6 A

SUBSTITUTING THIS VALUES IN   -- EQ - 1

X =    1.7355 * 10^ -10 * 0.18 / 4.6 * 10 ^ -10

= 6.7910 cms
here we took n = 1 as we need the distance of the first maxiam from the
centre
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