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15 April, 07:17

1. x-rays of wavelength 0.138nm fall on a crystal whose atoms, lying in planes, are spaced 0.285 nm apart. At what angle with the surface must the x-rays be directed if the a. first diffraction maximum is observed? b. second diffraction maximum is observed? c. third diffraction maximum is observed? g

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  1. 15 April, 09:48
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    a.) 25.8 degree

    b.) 44.1 degree

    c.) 55.5 degree.

    Explanation:

    Given that the

    Wavelength (λ) = 0.138 nm

    Spacing d = 0.285 nm

    Using the formula dtan Ø = n (λ)

    Where n = number of diffraction maximum observed

    1.) For the first diffraction maximum,

    Substitute the values into the formula where n = 1

    0.285 * 10^-9 * tanØ = 1 * 0.138 * 10^-9

    Tan Ø = 0.138/0.285

    Tan Ø = 0.4842

    Ø = tan^-1 (0.4842)

    Ø = 25.84 degree

    2.) For the second diffraction maximum

    Where n = 2

    0.285 * 10^-9 * tanØ = 2 * 0.138 * 10^-9

    Tan Ø = 0.276/0.285

    Tan Ø = 0.9684

    Ø = tan^-1 (0.9684)

    Ø = 44.1 degree

    3.) For the third diffraction maximum

    Where n = 3

    0.285 * 10^-9 * tanØ = 3 * 0.138 * 10^-9

    Tan Ø = 0.414/0.285

    Tan Ø = 1.4526

    Ø = tan^-1 (1.4526)

    Ø = 55.5 degree
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