Question

A radioactive isotope of mercury decays into gold with a decay constant of 0.018. (a) Calculate its half life (b) what fraction of this original amount will remain after three half life (c) after 10 days.
Please give its answer of this numerical

Answer 1

Answer on Question #72359, Physics / Atomic and Nuclear Physics

A radioactive isotope of mercury decays into gold with a decay constant of 0.018. (a) Calculate its half-life (b) what fraction of this original amount will remain after three half-life (c) after 10 days.

Answer:

a)

The decay constant is $r = 0.018$.

$$t_{1/2} = \frac{\ln 2}{r}$$ $$t_{1/2} = \frac{0.693}{0.018} = 38.5 \text{ hour}$$

b)

$$N = \frac{1}{2} N_0$$

So

$$N = \left(\frac{1}{2}\right)^3 N_0 = \frac{1}{8} N_0 = 0.125$$

c)

10 days = 240 hours

$$\frac{N}{N_0} = 2^{-\frac{t}{T}}$$ $$\frac{N}{N_0} = 2^{-\frac{240}{35.5}} = 0.133$$

Answer: a) 38.5; b) 0.125; c) 0.133

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