Now try a real-world example with more than 100 atoms. Start with 5.4 × 1012 radioactive nuclei of Lincolnium. Approximately how many nuclei would still be radioactive after four half-life cycles?
Answer is: number of radioactive nuclei of Lincolnium is 3.375×10¹¹.
Half-life is the time required for a quantity (in this example number of radioactive nuclei of lincolnium) to reduce to half its initial value. Initial number of nuclei: 5.4×10¹². After first half-life: 50% · 5.4×10¹² ÷ 100% = 2.7×10¹². After second half-life: 0.5 · 2.7×10¹² = 1.35×10¹². After third half-life: 0.5 · 1.35×10¹² = 6.75×10¹¹. After fourth half-life: 0.5 · 6.75×10¹¹ = 3.375×10¹¹.
