Question
Represent graphically log10 (activity /dps) versus t/s. What is its slope ?
✓
Answer
Equation for a decay constant $(\lambda)$ is given as,
$
\lambda=\frac{2.303}{ t } \log _{10} \frac{ N _0}{ N }
$
From equation (i),
$
\log _{10} N =\frac{-\lambda}{2.303} t +\log _{10} N _0
$
On comparing with $y = m x+ c , y =\log _{10} N , m =\frac{-\lambda}{2.303}, x= t , c =\log _{10} N _0$
Now, $N \propto\left(\frac{- dN }{ dt }\right) \quad$
Hence, instead if $\log _{10} N$ versus t, $\log _{10}\left(\frac{- dN }{ dt }\right)$ which is $\log _{10}$ (activity) is plotted.
The graph of $\log _{10}$ (activity/dps) versus t/s gives a straight line which can be represented as follows:
$
\lambda=\frac{2.303}{ t } \log _{10} \frac{ N _0}{ N }
$
From equation (i),
$
\log _{10} N =\frac{-\lambda}{2.303} t +\log _{10} N _0
$
On comparing with $y = m x+ c , y =\log _{10} N , m =\frac{-\lambda}{2.303}, x= t , c =\log _{10} N _0$
Now, $N \propto\left(\frac{- dN }{ dt }\right) \quad$
Hence, instead if $\log _{10} N$ versus t, $\log _{10}\left(\frac{- dN }{ dt }\right)$ which is $\log _{10}$ (activity) is plotted.
The graph of $\log _{10}$ (activity/dps) versus t/s gives a straight line which can be represented as follows:
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