If a strong diffraction peak is observed when electrons are incident at an angle ‘ i ’ from the normal to the crystal planes with distance ‘ d ’ between them, de Broglie wavelength λ_dB of electrons can be calculated by the relationship ( n is an integer):

Bragg's law is usually 2d θ = nλ , where θ is the glancing angle with the plane.If i is the angle with the normal, then θ = 90^- i .Substituting θ : 2d (90^- i) = nλ 2d i = nλ_dB (Wait, the options provided in text mark (4). Let's re-verify. Usually, path difference is 2d i . If the question implies one plane, it's different, but for crystal planes, it's 2d i .)

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If a strong diffraction peak is observed when electrons are incident at an angle ‘ ’ from the normal to the crystal planes with distance ‘ ’ between them, de Broglie wavelength of electrons can be calculated by the relationship ( is an integer):

A $d sin i = n λ_{d B}$
B $2 d cos i = n λ_{d B}$
C $2 d sin i = n λ_{d B}$
D $d cos i = n λ_{d B}$

Solution & Step-by-step Explanation

Bragg's law is usually 2 d sin θ = nλ, where θ is the glancing angle with the plane.If i is the angle with the normal, then θ = 9 0^{\circ} - i .Substituting θ : 2 d sin (9 0^{\circ} - i) = nλ ⟹ 2 d cos i = n λ_{d B} (Wait, the options provided in text mark (4). Let's re-verify. Usually, path difference is 2 d cos i . If the question implies one plane, it's different, but for crystal planes, it's 2 d cos i .)

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If a strong diffraction peak is observed when electrons are incident at an angle ‘ ’ from the normal to the crystal planes with distance ‘ ’ between them, de Broglie wavelength of electrons can be calculated by the relationship ( is an integer):

d sin i = n λ_{d B}

2 d cos i = n λ_{d B}

2 d sin i = n λ_{d B}

d cos i = n λ_{d B}

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If a strong diffraction peak is observed when electrons are incident at an angle ‘ $i$ ’ from the normal to the crystal planes with distance ‘ $d$ ’ between them, de Broglie wavelength $λ_{d B}$ of electrons can be calculated by the relationship ( $n$ is an integer):

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If a strong diffraction peak is observed when electrons are incident at an angle ‘i ’ from the normal to the crystal planes with distance ‘d ’ between them, de Broglie wavelength λdB​ of electrons can be calculated by the relationship (n is an integer):

Solution & Step-by-step Explanation

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Discussion

If a strong diffraction peak is observed when electrons are incident at an angle ‘ $i$ ’ from the normal to the crystal planes with distance ‘ $d$ ’ between them, de Broglie wavelength $λ_{d B}$ of electrons can be calculated by the relationship ( $n$ is an integer):