Question

A radioactive nuclei X decays simultaneously to two nuclei Y and Z as:

t_½ is 12 minutes while t'_½ is 3 minutes. Find the time in which nuclei X decays 50%.

• A. 4.8 minutes
• B. 15 minutes
• C. 2.4 minutes
• D. 9 minutes

Answer 1

The Correct Option is C

To solve the given problem, we need to determine the effective half-life of the radioactive nuclei X that decays simultaneously into two products, Y and Z.

The half-life for decay into Y (t_{1/2}) is 12 minutes and for decay into Z (t'_{1/2}) is 3 minutes. The formula for effective half-life (t_{\text{eff}}) in such cases is given by:

\frac{1}{t_{\text{eff}}} = \frac{1}{t_{1/2}} + \frac{1}{t'_{1/2}}

Substitute the given values:

\frac{1}{t_{\text{eff}}} = \frac{1}{12} + \frac{1}{3}

\frac{1}{t_{\text{eff}}} = \frac{1}{12} + \frac{4}{12} = \frac{5}{12}

Therefore:

t_{\text{eff}} = \frac{12}{5} = 2.4 \text{ minutes}

The time taken for X to decay 50% is the effective half-life, which is 2.4 minutes.

Thus, the correct answer is 2.4 minutes.