The intensity of γ - radiation from a given source is I . On passing through 36 mm of lead, it is reduced to I 8 . Assuming that the intensity in transmitted radiation varies exponentially with the thickness of the material, then the thickness of lead, which will reduce the intensity to I 2 , will be

Step-by-step solution

On passing through lead, the intensity of γ - radiation decreases exponentially with the thickness traversed and is given by I = I 0 e - μ x , where μ is the absorption coefficient of the lead. In the first case, when x = 36   mm , I = I 0 8 I 0 8 = I 0   e - μ × 36 ⇒ log e 8 = 36 μ In the second case, I = I 0 2 Let x be the thickness of the lead sheet, then I 0 2 = I 0   e - μ x log e ⁡ 2 = μ x μ x 36 μ = log e 2 log e 8 x = 36 × log