A newly prepared radioactive source with a half-life of 2 h emits radiation at an intensity 64 times the allowable safe level. The minimum time required before one can safely work with this source is

Step-by-step solution

Let the safe level of radiation intensity be I₀ . The initial intensity of the radioactive source is I = 64 I₀ . The intensity after n half-lives is given by I(t) = I ( 1 2 )^n . For the source to be safe to work with, we require I(t) I₀ . 64 I₀ ( 1 2 )^n I₀ 64 2^n 1 2^n 64 Since 64 = 2^6 , we get n = 6 . The minimum number of half-lives required is 6 . Given the half-life T_ 1/2 = 2 h , the minimum time required is t = n T_ 1/2 = 6 2 h = 12 h .