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You have discovered a new radioisotope 19X with half life of 14.2 days. How long would it take a solution containing 42000 dpm to decay to 500 dpm?You have discovered a new radioisotope 19X with half life of 14.2 days. How long would it take a solution containing 42000 dpm to decay to 500 dpm?

You have discovered a new radioisotope 19X with half life of 14.2 days. How long would it take a solution containing 42000 dpm to decay to 500 dpm?You have discovered a new radioisotope 19X with half life of 14.2 days. How long would it take a solution containing 42000 dpm to decay to 500 dpm?

Grade:12th pass

1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
6 years ago
Dear student,
The formula to be used goes as follows:
t=\frac{1}{\lambda}\ln\frac{N_0}{N}
Also, we know:
\lambda=\frac{0.693}{t_{1/2}}=0.693/14.2
thus,
t=\frac{1}{\lambda}\ln\frac{N_0}{N}=\frac{14.2}{0.693}\ln\frac{42000}{500}=90.79 days

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