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NEET CHEMISTRYChemical KineticsEasy

Question

The radioisotope, tritium (13H^3_1H) has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years:

A

1 mg

B

2 mg

C

4 mg

D

8 mg

Step-by-Step Solution

Radioactive decay follows first-order kinetics. The amount of radioactive substance remaining (NN) after nn half-lives is given by the formula:

N=N02nN = \frac{N_0}{2^n}

where N0N_0 is the initial amount of the substance.

Given: Initial amount, N0=32 mgN_0 = 32 \text{ mg} Half-life, t1/2=12.3 yearst_{1/2} = 12.3 \text{ years} Total time, t=49.2 yearst = 49.2 \text{ years}

First, calculate the number of half-lives (nn): n=tt1/2=49.2 years12.3 years=4n = \frac{t}{t_{1/2}} = \frac{49.2 \text{ years}}{12.3 \text{ years}} = 4

Now, substitute the values into the formula to find the remaining amount: N=3224=3216=2 mgN = \frac{32}{2^4} = \frac{32}{16} = 2 \text{ mg}

Therefore, 2 mg of tritium would remain after 49.2 years.

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Chemical Kinetics. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

CHEMISTRYChemical Kineticsradioisotopetritiumhalflifeinitialamount

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