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H@z@r@h
Lv 5
H@z@r@h asked in Science & MathematicsPhysics · 1 decade ago

X-Rays. Help Me To Solve This Question?

If a beam of X-rays is incident upon material that has an absorption coefficient of 200 cm^-1, what thickness is necessary to reduce the number of emerging x-ray photons to one-half of the number of incident photons?

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  • Karl
    Lv 6
    1 decade ago
    Favorite Answer

    The intensity of an x-ray source going through matter is given by

    I/I(0) = e^(-kx)

    I = intensity

    I(0) = Initial intensity at depth zero

    k = attenuation coefficient = 200 cm^-1

    We want x such that e^(-kx) = 1/2, or such that e^kx = 2.

    Take natural logs of both sides:

    ln(2) = 200x

    0.693 = 200x

    0.693/200 = x = 3.465 * 10^-3 cm

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