Question

The half life (T) and the disintegration constant $(\lambda)$ of a radioactive substance are related as.

• A. $\lambda T = 1$
• B. $\lambda T = 0.693$
• C. $\frac{T}{\lambda} = 0.693$
• D. $\frac{\lambda}{T} = 0.693$

Answer 1

Answer: (B)

$\lambda T = 0.693$

Answer 2

By using $N = N_{0}e^{- \lambda t}$ ⇒ $\frac{N_{0}}{2} = N_{0}e^{- \lambda T_{1/2}}$⇒ $2 = e^{\lambda T_{1/2}}$

By taking log_e both the side

$\log_{e}2 = \lambda T_{1/2}$ ⇒ $\lambda T_{1/2} = 0.693$