Question

Starting with a sample of pure $ ^{66} Cu, $ 7/8 of its decays into Zn in 15 min. The corresponding half-life is

• A. 10 min
• B. 15 min
• C. 5 min
• D. $ 7 \frac{1}{2} min $

Answer 1

The Correct Option is C

If N is the number of disintegrated nucleus in time t. then $ N = N_0 (1 - e^{- \lambda t} ) $ $ \Rightarrow \frac{N_0 - N}{N_0} = e^{- \lambda t} $ $ \therefore \frac{1}{8} = e^{- \lambda t} $ $ \Rightarrow 8 = e^{\lambda t} $ $ \Rightarrow 3 ln 2 = \lambda t $ $ \Rightarrow \lambda = \frac{3 \times 0.693}{15} $ Half-life period $ t_{t/2} = \frac{0.693}{3 \times 0.693} \times 15 $ $ t_{t/2} = 5 min $