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:

Option 1 - 3.75 hours

Option 2 - 0.56 hours

Option 3 - 0.26 hours

Option 4 - 1.80 hours

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Answered by

Vishal Baghel | Contributor-Level 10

8 months ago

Correct Option - 4

Detailed Solution:

$\frac{1}{t} = \frac{1}{t_{1}} + \frac{1}{t_{2}}$

$\frac{1}{t} = \frac{1}{3} = \frac{1}{4.5}$

$= \frac{4.5 + 3}{3 * 4.5}$

t = $\frac{3 * 4.5}{7.5} = \frac{9}{5}$

t = 1.8 hrs

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