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The half-life of ⁶⁵ Zn is 245 days. After x days, 75 % of original activity remained. The value of x in days is _ _ _ _ . (Nearest integer) (Given: 3=0.4771 and 2=0.3010 )

Correct answer

0

Step-by-step solution

Using radioactive decay: A = A₀ ( 1 2 )^ t/t_ 1/2 . With 75% activity remaining: 0.75 = ( 1 2 )^ x/245 . Taking log base 10: (0.75) = x 245 (0.5) . Calculate: (0.75) = 3 - 4 = 0.4771 - 2(0.3010) = -0.1249 and (0.5) = -0.3010 . Thus -0.1249 = x 245 (-0.3010) , giving x = 0.1249 245 0.3010 = 101.66 102 days (nearest integer).

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