Question

Half-life of radon is 3.5 days. The amount of radon left out of 12 mg mass undecayed after 35 days is nearly

• A. $0.006$ mg
• B. $0.012$ mg
• C. $0.024$ mg
• D. $0.036$ mg
• E. $0.048$ mg

Hint:

The remaining mass in radioactive decay follows an exponential law based on the number of half-lives.

Answer 1

The Correct Option is B

Step 1: The amount of a substance remaining after $n$ half-lives is given by: \[ N = N_0 \times \left(\frac{1}{2}\right)^n \] where $N_0$ is the initial mass, and $n$ is the number of half-lives elapsed. 
Step 2: Given: \[ N_0 = 12 { mg}, \quad T_{1/2} = 3.5 { days}, \quad t = 35 { days} \] \[ n = \frac{t}{T_{1/2}} = \frac{35}{3.5} = 10 \] 
Step 3: Calculate remaining mass: \[ N = 12 \times \left(\frac{1}{2}\right)^{10} \] 
Step 4: \[ \left(\frac{1}{2}\right)^{10} = \frac{1}{1024} \approx 0.00098 \] \[ N = 12 \times 0.00098 = 0.0118 \approx 0.012 { mg} \] 
Step 5: Therefore, the correct answer is (B).