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

Answer: (C)

5 min

Answer 2

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 $t_{t/2} = \frac{0.693}{3 \times 0.693} \times 15$ $t_{t/2} = 5 min$