Question

The relation between half life $(T)$ and decay constant $(\lambda)$ is

• A. $\lambda T=1$
• B. $\lambda T =\frac{1}{2}$
• C. $\lambda T =\log _{ e } 2$
• D. $\lambda=\log 2 T$

Answer 1

Answer: (C)

$\lambda T =\log _{ e } 2$

Answer 2

By radioactive decay law. The time in which the final amount becomes half of its initial value is called half-life $(T)$ of that radioactive element. Relation between half-life and disintegration (decay) constant is given $T=\frac{0.6931}{\lambda}$ $\Rightarrow T= \frac{\log _{e} 2}{\lambda}$ So, $\lambda T=\log _{e} 2$