Question 209: Dual Nature of Matter and Radiation

Question

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see figure).
Electrons accelerated by potential $$V$$ are diffracted from a crystal. If $$d = 1\mathop A\limits^ \circ  $$ and $$i = {30^ \circ },\,\,\,V$$ should be about
$$\left( {h = 6.6 	imes {{10}^{ - 34}}Js,{m_e} = 9.1 	imes {{10}^{ - 31}}kg,\,e = 1.6 	imes {{10}^{ - 19}}C} ight)$$

Accepted Answer

Using Bragg's equation $$2d$$ $$\sin 	heta  = n\lambda $$
Here $$n=1,$$ $$	heta  = 90 - i = 90 - 30 = {60^ \circ }$$
$$	herefore$$ $$2d$$ $$\sin \,	heta \, = \lambda \,\,\,\,\,\,\,\,\,\,....\left( i ight)$$
Also, $$\lambda  = {{12.27} \over {\sqrt V }} 	imes {10^{ - 10}}m\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)$$
From $$(i)$$  &  $$(ii)$$  $$2 	imes {10^{ - 10}} 	imes \sin {60^ \circ } = {{12.27} \over {\sqrt V }} 	imes {10^{ - 10}}$$
$$V = {{{{\left( {12.27} ight)}^2}} \over 3} = 50V$$

Answer

$$2000$$ $$V$$

Answer

$$50$$ $$V$$

Answer

$$500$$ $$V$$

Answer

$$1000$$ $$V$$

Dual Nature of Matter and Radiation

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