Question

The half-life of radioactive Radon is 3.8 days. The time at the end of which \( \frac{1}{20} \)th of the radon sample will remain undecayed is given (using \( \log_e = 0.4343 \))

• A. 3.8 days
• B. 16.5 days
• C. 33 days
• D. 76 days

Hint:

The half-life of a radioactive substance is related to the time it takes for half of the substance to decay, and it can be used to calculate the remaining quantity over time.

Answer 1

The Correct Option is C

Step 1: Radioactive Decay Formula.
The amount of substance remaining after time \( t \) is given by: \[ N_t = N_0 e^{-t/\tau} \] where \( \tau \) is the mean life and \( t \) is the time. The relationship between the half-life \( t_{1/2} \) and the mean life \( \tau \) is: \[ t_{1/2} = 0.693 \tau \] Given that the half-life of Radon is 3.8 days, we can calculate the time for \( \frac{1}{20} \)th of the sample to remain undecayed using the decay equation. Step 2: Conclusion.
The correct answer is (C), 33 days.