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NEET CHEMISTRYStructure of AtomEasy

Question

If the radius of the second Bohr orbit of the He+He^+ ion is 105.8 pm105.8 \text{ pm}, what is the radius of the third Bohr orbit of the Li2+Li^{2+} ion?

A

158.7 Å

B

158.7 pm

C

15.87 pm

D

1.587 pm

Step-by-Step Solution

The radius (rnr_n) of the nn-th orbit for a hydrogen-like species with atomic number ZZ is given by the expression: rn=52.9n2Z pmr_n = \frac{52.9 n^2}{Z} \text{ pm}

  1. Verify the Given Data for Helium Ion (He+He^+): For Helium (HeHe), atomic number Z=2Z = 2. For the second orbit, n=2n = 2. r2(He+)=52.9×(2)22=52.9×2=105.8 pmr_{2}(He^+) = \frac{52.9 \times (2)^2}{2} = 52.9 \times 2 = 105.8 \text{ pm} This matches the value given in the question.

  2. Calculate Radius for Lithium Ion (Li2+Li^{2+}): For Lithium (LiLi), atomic number Z=3Z = 3. For the third orbit, n=3n = 3. r3(Li2+)=52.9×(3)23r_{3}(Li^{2+}) = \frac{52.9 \times (3)^2}{3} r3(Li2+)=52.9×93=52.9×3r_{3}(Li^{2+}) = \frac{52.9 \times 9}{3} = 52.9 \times 3 r3(Li2+)=158.7 pmr_{3}(Li^{2+}) = 158.7 \text{ pm}

Exam Context & Concepts Covered

This question aligns with the NEET CHEMISTRY syllabus, specifically targeting concepts from Structure of Atom. 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.

CHEMISTRYStructure of Atomradiussecondradius

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