How much of 5g of radioactive element whose half life is 50days remains after 200days?

Analyze the question: We have 5 g of a radioactive element with a half-life of 50 days. We need the mass left after 200 days.

Concept: Half-life is the time it takes for half of a radioactive substance to decay. The remaining mass is:

N = N₀ × (1/2)^n, where n = total time ÷ half-life

Solution:

1. Number of half-lives: n = 200 ÷ 50 = 4

2. Halve the mass 4 times: • After 50 days: 5 ÷ 2 = 2.5 g • After 100 days: 2.5 ÷ 2 = 1.25 g • After 150 days: 1.25 ÷ 2 = 0.625 g • After 200 days: 0.625 ÷ 2 = 0.3125 g

3. Using the formula: N = 5 × (1/2)⁴ = 5 ÷ 16 = 0.3125 g ≈ 0.31 g

Answer: 0.31 g, which is option D.

Tip: For half-life questions, first find the number of half-lives (time ÷ half-life), then divide the original mass by 2ⁿ. Here, 2⁴ = 16, so 5 ÷ 16 ≈ 0.31 g. Halving step by step, as in the table above, is a quick way to check your work and avoid mistakes in the exam hall.