Question

With the following data, estimate the half-life of an unknown, and suggest what isotope it is (see a table for a list of possible isotopes) (the correct answer is 1.82 h , argon-41. I just do not know how to get it. thank you)

time (s) | counting rate (counts/s) |

0 | 200 |

1000 | 182 |

2000 | 162 |

3000 | 144 |

4000 | 131 |

Answer #1

**Let the concentration be C1 at time t1 and C2 at time
t2**

**Then according to the equation we can write**

**
------ (i)**

** -------
(ii)**

**Divide equation 1 by equation 2 we get**

**Taking ln both sides we get**

**Now coming back to part (b) of the equation**

**b) Using the table we can write**

**Hence Lambda * No = 200**

**Now we can write the other equation**

**182 = 200 * e^(-1000*lambda)**

**ln(200/182) = 1000 * lambda**

**lambda = 9.431 * 10^(-5)**

**100 = 200 * e^(-t*9.431*10^(-5))**

**ln2 = t * 9.431 * 10^(-5)**

**t = 7348.21 seconds**

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