Q.49 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.
1 gram radioactive nuclei (300-day half-life) after 900 days
Quick Solution
The weight of radioactive nuclei remaining after 900 days is 125.0 mg. This result follows from the principles of exponential radioactive decay, where exactly three half-lives elapse for a sample with a 300-day half-life.
Decay Calculation
Radioactive decay reduces the number of undecayed nuclei by half every half-life period. With a half-life t₁/₂ = 300 days and total time t = 900 days, the number of half-lives is n = t/t₁/₂ = 900/300 = 3.
Remaining fraction: (1/2)ⁿ = (1/2)³ = 1/8 = 0.125
Remaining mass: 1g × 0.125 = 0.125g = 125.0 mg
Step-by-Step Breakdown
- After 1 half-life (300 days):
1000 × 1/2 = 500 mgremains. - After 2 half-lives (600 days):
500 × 1/2 = 250 mgremains. - After 3 half-lives (900 days):
250 × 1/2 = 125.0 mgremains.
This iterative halving confirms the exponential nature of decay, independent of the “open container” detail.
Decay Timeline Table
| Time (days) | Half-Lives | Remaining (mg) |
|---|---|---|
| 0 | 0 | 1000.0 |
| 300 | 1 | 500.0 |
| 600 | 2 | 250.0 |
| 900 | 3 | 125.0 |
CSIR NET Exam Tips
- Practice radioactive decay problems with half-life periods like 300 days over 900 days.
- Use
n = t/t₁/₂for quick integer checks; verify to 1 decimal place. - Open container implies no containment issues—focus on decay kinetics.
Core Formula
General Formula: N = N₀ × (1/2)^(t/t₁/₂)
Where:
N= remaining amountN₀= initial amount (1g = 1000mg)t= total time (900 days)t₁/₂= half-life (300 days)
