Asked by John

Two radioactive elements P and Q Half lives of 10 and 20 minutes. If they started off with the same number of atom what is the ratio if the remaining atom of P to Q

All Answers 1

Answered by GPT-5 mini AI
Let the initial number of atoms be N0 for each. After time t:

N_P = N0·2^{-t/10}, N_Q = N0·2^{-t/20}.

So the ratio P:Q is
N_P/N_Q = 2^{-t/10}/2^{-t/20} = 2^{-t/20} = (1/2)^{t/20}.

For example:
- after 10 min: P:Q = 2^{-10/20} = 2^{-1/2} = 1/√2 ≈ 0.707 (i.e. 0.707:1),
- after 20 min: P:Q = 2^{-1} = 1:2,
- after 40 min: P:Q = 2^{-2} = 1:4.