Half Life Formula
Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time. The mathematical representation of Half life is given below.
The formula for half life is,
\[t_{\frac{1}{2}}=\frac{ln2}{\lambda}=\frac{0.693}{\lambda}\]
Where,
\(\begin{array}{l}t_{\frac{1}{2}}\end{array} \)
is half life\(\begin{array}{l}\lambda\end{array} \)
is the disintegration constant
Solved Examples
Question 1: Calculate the half life of a radioactive substance whose disintegration constant is 0.002 years-1 ?
Solution:
Given quantities are,
\(\begin{array}{l}\lambda\end{array} \) = 0.002years-1
Half life equation is,
\(\begin{array}{l}t_{\frac{1}{2}}\end{array} \)
= \(\begin{array}{l}\frac{0.693}{\lambda }\end{array} \)
\(\begin{array}{l}t_{\frac{1}{2}}\end{array} \)
= \(\begin{array}{l}\frac{0.693}{0.002}\end{array} \)
= 346.5 years
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