Q. Two radioactive nuclei P and Q in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4N₀ and that of Q are N₀. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample would be
A) 5N₀/2
B) 2N₀
C) 3N₀
D) 9N₀/2
Explanation
[Solution from source] P: 4N₀(1/2)^t and Q: N₀(1/2)^(t/2) with t in minutes. Setting them equal gives 2^(2 − t) = 2^(−t/2), so t = 4 min, when P = Q = N₀/4. R = 5N₀ − N₀/2 = 9N₀/2. 5N₀/2 would count only the decayed P nuclei incorrectly. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.