question_answer

Define the term 'Activity' of a radio- active substance. State its \[SI\] unit. Two different radioactive elements with half lives \[{{T}_{1}}\] and \[{{T}_{2}}\] have \[{{N}_{1}}\] and \[{{N}_{2}}\] (undecayed) atoms respectively present at a given instant. Determine the ratio of their activities at this instant.                  

Answer:

                The activity of a sample is defined as the number of radioactive disintegrations taking place per second at any instant in the sample. Its \[SI\]unit is becquerel. \[1\]becquerel \[=1Bq=1\]decay per second. \[R=\frac{dN}{dt}=\lambda N=\frac{0.693}{{{T}_{1/2}}}N\] For sample 1, \[{{R}_{1}}=\frac{0.693}{{{T}_{1}}}{{N}_{1}}\] For sample 2, \[{{R}_{2}}=\frac{0.693}{{{T}_{2}}}{{N}_{2}}\] \[\therefore \]  \[\frac{{{R}_{1}}}{{{R}_{2}}}=\frac{{{N}_{1}}{{T}_{2}}}{{{N}_{2}}{{T}_{1}}}\]