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Structure of Atom question

2021 · 26 Aug · Shift 1 · Q10
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Structure of Atom question

2021 · 26 Aug · Shift 1 · Q10

JEE MainChemistryStructure of AtomMCQ+4 / −1
Given below are two statements. 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 principal quantum number. In the light of the above statements, choose the most appropriate answer from the options given below :
  1. A
    Both Statement I and Statement II are false
  2. B
    Both Statement I and Statement II are true
  3. C
    Statement I is false but Statement II is true
  4. D
    Statement I is true but Statement II is false
View written solutionFree

Correct answer: C

  1. Use Bohr model expression for electron velocity

    For a hydrogen-like species, the speed of the electron in the nthn^{\text{th}}nth orbit is vn=Ze22ε0h⋅1nv_n = \frac{Z e^2}{2\varepsilon_0 h}\cdot \frac{1}{n}vn​=2ε0​hZe2​⋅n1​ or simply, vn∝Znv_n \propto \frac{Z}{n}vn​∝nZ​ where:

    • ZZZ = positive charge on nucleus (atomic number)
    • nnn = principal quantum number

  2. Check Statement I

    Statement I says: velocity of electron increases with decrease in positive charge on the nucleus.

    But from vn∝Zv_n \propto Zvn​∝Z we see that if ZZZ decreases, then vnv_nvn​ also decreases, not increases.

    So, Statement I is false.

  3. Check Statement II

    Statement II says: velocity of electron increases with decrease in principal quantum number.

    From vn∝1nv_n \propto \frac{1}{n}vn​∝n1​ if nnn decreases, then vnv_nvn​ increases.

    So, Statement II is true.

  4. Choose the correct option

    • Statement I: False
    • Statement II: True

    Therefore, the correct option is: C\boxed{\text{C}}C​

  5. Comparison with stored answer

    Stored correct answer: C

    My derived answer matches the stored answer.

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