A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years, respectively. What will be the time after the which one third of the material remains ? (Take ln 3 = 1 . 1 )

Question

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years, respectively. What will be the time after the which one third of the material remains ? (Take ln 3 = 1 . 1 ), 1110 years, 700 years, 340 years, 740 years

MARKS App · Accepted Answer

Given λ 1 = ℓ n 2 700 / year λ 2 = ℓ n 2 1400 / year ∴ λ net = λ 1 + λ 2 = ln 2 1 700 + 1 1400 = 3 ln 2 1400 / year Now, let initial number of radioactive nuclei be N 0 , ∴ N 0 3 = N 0 e - λ mat t ⇒ ℓ n 1 3 = - λ net t ⇒ 1 . 1 = 3 × 0 . 693 1400 t ⇒ t ≈ 740 years Hence, option 4 .

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