Half-life is a key concept in understanding radioactive decay. It refers to the time required for half of the radioactive atoms in a sample to decay. This intrinsic property depends solely on the nature of the isotopic element, not on external conditions or measurement techniques.
For example, in the case of Ba-137m, the half-life is specific to this isotope and remains constant irrespective of how far or close it is to the Geiger tube. Thus, when considering experimental setups or modifications such as changes in distance to the detector, the half-life value remains unaffected.
The reason for this invariance is because half-life is a measure of the probability of decay, which is an inherent characteristic of the isotope's nucleus. Calculations involving half-life can be performed using the decay formula:
- \( N(t) = N_0 \times e^{-\lambda t} \)
where \( N(t) \) is the remaining number of radioactive nuclei at time \( t \), \( N_0 \) is the initial number, and \( \lambda \) is the decay constant related to the half-life by \( \lambda = \frac{\ln(2)}{T_{1/2}} \).
Thus, in our experiment, while the count rate might increase due to a closer placement of the radioactive source, the half-life itself, derived from the slope of the decay curve on a semi-log scale, remains constant.