Question

One gram of radioactive nuclei with a half-life of 300 days is kept in an open container. The weight of nuclei remaining after 900 days (correct to 1 decimal place) is .............. mg.

Hint:

After n half-lives, remaining mass = $M_0 / 2^n$.

Answer 1

Correct Answer: 124

Step 1: Determine number of half-lives.
Half-life = 300 days Time elapsed = 900 days \[ n = \frac{900}{300} = 3 \] Step 2: Apply decay formula.
Remaining mass = \[ 1\ \text{g} \times \left(\frac{1}{2}\right)^3 = \frac{1}{8} = 0.125\ \text{g} \] Step 3: Convert to mg.
\[ 0.125\ \text{g} = 125\ \text{mg} \] Step 4: Conclusion.
Mass remaining = 125.0 mg.