Question 223: Atoms & Nuclei

Question

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

Accepted Answer

$${{dA} \over {dt}} - ( - {\lambda _1}A) + ( - {\lambda _2}A)$$
$$ \Rightarrow {{dA} \over {dt}} =  - ({\lambda _1} + {\lambda _2})A$$
$$ \Rightarrow {\lambda _{eff}} = {\lambda _1} + {\lambda _2}$$
$$ \Rightarrow {{\ln 2} \over {{{({t_{1/2}})}_{eff}}}} = {{\ln 2} \over {{{({t_{1/2}})}_1}}} + {{\ln 2} \over {{{({t_{1/2}})}_2}}}$$
$$ \Rightarrow {({t_{1/2}})_{eff}} = {{4.5 	imes 3} \over {7.5}}$$ hours = 1.8 hours

Answer

3.75 hours

Answer

0.56 hours

Answer

0.26 hours

Answer

1.80 hours

Atoms & Nuclei

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

Choose the correct answer: