The intensity of gamma radiation from a given source is I . On passing through 36 mm of lead, it is reduced to I /8 . The thickness of lead which will reduce the intensity to I /2 will be

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​ ∵ I = I 0 ​ e − k x ⇒ I 0 ​ I ​ = e − k x ∴ ln ( I 0 ​ I ​ ) = − k x ​ In first case ​ ln ( 8 1 ​ ) = − k × 36 ln ( 2 − 3 ) = − k × 36 or 3 ln 2 = k × 36 ​ In second case, ln ( 2 1 ​ ) = − k × x or ln ( 2 − 1 ) = − k x or ln 2 = k x From (i) and (ii) 3 × ( k x ) = k × 36 or x = 12 mm .

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