Question

A radioactive element X converts into another stable element Y. Half-life of X is 2 hours. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1:4. Then t, in hours is:

• A. 2
• B. between 4 and 6
• C. 4
• D. 6

Hint:

Use decay ratio directly to avoid lengthy calculations.

Answer 1

The Correct Option is B

Step 1: Let initial atoms be N₀.
Step 2: Given ratio: (NX)/(NY) = (1)/(4) ⟹ NX = (N₀)/(5)
Step 3: Radioactive decay law: (NX)/(N₀) = ((1)/(2))ᵗ/2 = (1)/(5) ⟹ t ≈ 4.6h