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:

• A. 3.75 hours
• B. 0.56 hours
• C. 0.26 hours
• D. 1.80 hours

Answer 1

Answer: (D)

1.80 hours

Answer 2

The correct answer is (D): 1.80 hours

Explanation:

$\frac{dA }{dt }$- (-λ1 A) + ( -λ2 A)
_⇒ $\frac{dA }{dt }$ = - ( λ1 + λ2 _)A
⇒ λeff = λ1 + λ2
_⇒ $\frac{ln2}{(t_{1/2})eff }$ = $\frac{ln2}{(t_{1/2})_1}$ _ + $\frac{ln2}{(t_{1/2})_2}$
_⇒ _$( t_{1/2} )$eff =$\frac{ 4.5 × 3 }{7.5}$ hours
= 1.8 hours