Question

Half life of radon is 3.82 d. by whhat time would 99.9% of radon will be decayed

Answer 1

Answer

38.171 days

Explanation:

1st off, the important concept here is,

all decay reactions are 1st order reactions

we have to deal this in 2 steps

   1) find k (rate constant) using given half life

   2) using k , find out rate using integrated rate equation\

1)

$t_{1/2}  = \frac{ln2}{k}  = \frac{0.693}{k} =$ 3.82 days

k = 0.693 /3.82 = 0.181

2)

$k = \frac{2.303}{t} log\frac{A_{0} }{A_{t}}$

where $A_{0}   A_{t}$ are initial and final concentrations respectively

$t = \frac{2.303}{0.181}  log \frac{100}{100-99.9}$ (assuming 100 is initial and 99.9 is final concentrations)

t = 38.171 days

therefore for completion of 99.9% reaction , it would take 38.171 days

to get time in

hours = t * 24 = 916.1 hours

minutes = t * 1440 = 54,966 minutes

seconds = t * 86400 =  33,00,000 seconds approximately