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  • Please help! - Dual Nature of Matter and Radiation - JEE Main

Question is based on the following paragraph.

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).

Question : Electrons accelerated by potential V are diffracted from a crystal. If  d=1\; \dot{A}\; and \; i=30^{\circ},V   should be about  (h=6.6\times 10^{-34} \; Js,m_{e}=9.1\times 10^{-31}kg,e=1.6\times 10^{-19}C)

 

Option 1)

1000 V

 Option 2)

2000 V
Option 3)

50 V

 Option 4)

500 V

Answers (1)

best_answer

As we learnt in

Bragg’s formula -

2d\sin \Theta = n\lambda

 

- wherein

d-distance\: between \: diffracting\: planes

\Theta = \frac{180-\phi }{2}

\lambda = 1.65 A^{\circ}

 

 

 Condition of constructive interference is 2d\ sin\theta=n{\lambda}

\theta=90^{o}-i=60^{o}

Take n = 1

&   \lambda=\frac{h}{\sqrt{2mE}}=\frac{h}{\sqrt{2meV}}

\therefore\ \;\frac{h}{\sqrt{2meV}}=\frac{2\times{1\AA\times{\sqrt{3}}}}{2}

Square both side

    \frac{h^{2}}{2meV}=3\times10^{-20}

V=\frac{\left(6.62\times10^{-34} \right )^{2}}{2\times9.1\times10^{-31}\times1.6\times10^{-19}\times3\times10^{-20}}=\frac{43.82\times10^{-68}}{87.36\times10^{-70}}=50V

Correct option is 3


Option 1)

1000 V

This is an incorrect option.

Option 2)

2000 V

This is an incorrect option.

Option 3)

50 V

This is the correct option.

Option 4)

500 V

This is an incorrect option.

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perimeter

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