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

The Correct Option is D

The correct answer is (D): 1.80 hours

Explanation:

\(\frac{dA }{dt }\)- (-λ₁A) + ( -λ2A)
⇒ \(\frac{dA }{dt }\) = - ( λ₁ + λ₂ )A
⇒ λ_eff = 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