JEE Main · 2021 · Shift-ImediumATOM-054

Statement I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with…

Structure of Atom · Class 11 · JEE Main Previous Year Question

Question

Statement I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus. Statement II: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principle quantum number.

Choose the most appropriate answer:

Options
  1. a

    Statement I is false but Statement II is true

  2. b

    Statement I is true but Statement II is false

  3. c

    Both Statement I and Statement II are false

  4. d

    Both Statement I and Statement II are true

Correct Answera

Statement I is false but Statement II is true

Detailed Solution

🧠 Dynamics of the Bohr Electron Bohr's velocity (vnv_n) is a balance of centrifugal force and nuclear attraction. The speed depends on how strong the "pull" is (ZZ) and how "far" the path is (nn).

🗺️ The Velocity Audit

  • Statement I: Claims velocity increases with decrease in positive charge (ZZ).
    • Check: vZ/nv \propto Z/n. If ZZ decreases, the pull is weaker, and the speed decreases. So, Statement I is False.
  • Statement II: Claims velocity increases with decrease in principal quantum number (nn).
    • Check: As nn decreases (electron gets closer to nucleus), the orbital speed must increase to stay in balance. v1/nv \propto 1/n. So, Statement II is True.

The Satellite Analogy Think of planets! Planets closer to the Sun (nn is small) move much faster than distant ones. And a massive Sun (ZZ is large) makes planets move faster. V=Large Z, Small nV = \text{Large } Z, \text{ Small } n.

⚠️ Common Traps Qualitative distractors! Words like "no strong hold" in I sounds plausible, but the mathematical proportionality vZv \propto Z is absolute. Don't let the physical "story" distract you from the formula.

Answer: (a)\boxed{\text{Answer: (a)}}

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