Question

A radioactive nuclide X decays into nuclei Y and Z by simultaneous disintegration as shown.Effective decay constant for the disintegration is

• A. ${\lambda }_1+{\lambda }_2$
• B. $\frac{{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$
• C. $\frac{{\lambda }_1+{\lambda }_2}{2}$
• D. $\frac{2{\lambda }_1{\lambda }_2}{{\lambda }_1+{\lambda }_2}$

Answer 1

The correct option is A ${\lambda }_1+{\lambda }_2$

Equation for parallel disintegration can be written as $-\frac{d{N}_X}{dt}={\lambda }_1{N}_X+{\lambda }_2{N}_X$
$⟹-\frac{d{N}_X}{dt}=({\lambda }_1+{\lambda }_2)N_X$
Effective decay in parallel disintegration is given by ${\lambda }_p={\lambda }_1+{\lambda }_2$