Half Life Formula

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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