Physics - Modern Physics Question with Solution | TestHub

$T_{aug}$=1/λ

$\text{1/}{\text{λ}}_{\text{α}}=\text{1620}\Rightarrow {\text{λ}}_{\text{α}}=\frac{1}{\text{1620 years}}$

$\text{1/}{\text{λ}}_{\text{β}}=\text{405}\Rightarrow {\text{λ}}_{\text{β}}=\frac{1}{\text{405 years}}$

${\text{N = No e}}^{-}\left({\text{λ}}_{\text{α}}+{\text{λ}}_{\text{β}}\right)\text{t}$

$\frac{\text{No}}{4}={\text{No e}}^{-}\left({\text{λ}}_{\text{α}}+{\text{λ}}_{\text{β}}\right)t$

${\text{2ln2}}^{}=\left[\frac{1}{\text{1620}}+\frac{1}{\text{405}}\right]t=\frac{\text{t}}{\text{324}}$

$\text{t}={\text{648 ln2}}^{}=\text{449 years}$