COMEDK · Chemistry · 19. Chemical Kinetics

The initial amount of 2 radioactive elements X and Y is 1 g each and their half-lives are 12 hours and 16 hours respectively. The ratio of X and Y after 2 days is:

A 0.043055555555556
B 0.084027777777778
C 0.04375
D 0.12569444444444

Verified Solution

Answer & Solution

Correct Answer

(A) 0.043055555555556

Step-by-step Solution

Detailed explanation

The amount of a radioactive substance remaining after time \(t\) is given by \(N(t) = N_0 \left( \dfrac{1}{2} \right)^{t/T_{1/2}}\), where \(N_0\) is the initial amount and \(T_{1/2}\) is the half-life. Given \(t = 2\) days = \(48\) hours. For element X: \(N_0 = 1\) g,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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