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. \(4\)
• C. between 4 and 6
• D. 6

Hint:

If only parent nuclei are present initially: NY = N₀ - NX Use this relation before applying decay law.

Answer 1

The Correct Option is B

Step 1: Let the initial number of atoms be N₀. After time t: NX = (N₀)/(5), NY = (4N₀)/(5)
Step 2: Radioactive decay law: NX = N₀((1)/(2))ᵗ/T_¹/²
Step 3: Substituting values: (1)/(5) = ((1)/(2))ᵗ/2
Step 4: Taking logarithm: (t)/(2) = log₂ 5 ≈ 2.32 ⟹ t ≈ 4.64h Closest option is 4h.