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ella [17]
3 years ago
8

The half life of an isotope X is 3 days how long will it take for 1/2 of a 10 G sample to decay

Chemistry
1 answer:
lorasvet [3.4K]3 years ago
3 0

Answer:  It will take 3 days for half of a 10 g sample to decay.

Explanation:

Half-life of sample of an isotope X = 3 days

\lambda=\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{3 days}=0.231 day^{-1}

N=N_o\times e^{-\lambda t}

\lnN=-\lambda t\lnN_o

Sample decayed = \frac{N_o}{2}=\frac{10 g}{2 g}=5 g

N=N^o-\text{sample decayed}=10 g-5 g=5 g, time = t

\ln[5 g]=-0.231 day^{-1}\times t\ln[10]

\ln[\frac{5}{10}]=-0.231\times t

\ln\frac{1}{2}=-0.693=-0.231\times t

t = 3 days

It will take 3 days for half of a 10 g sample to decay.

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