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Structure of Atom question

2021 · 17 Mar · Shift 1 · Q15
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Structure of Atom question

2021 · 17 Mar · Shift 1 · Q15

JEE MainChemistryStructure of AtomNumerical+4 / −1
A certain orbital has n = 4 and mL = −-− 3. The number of radial nodes in this orbital is ‾\underline{\hspace{2cm}}​. (Round off to the Nearest Integer).
Numerical answer
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Correct answer: 0

  1. Given quantum numbers

    We are given: n=4,ml=−3n = 4, \quad m_l = -3n=4,ml​=−3

  2. Find the allowed value of lll

    For a given azimuthal quantum number lll, the magnetic quantum number mlm_lml​ can take values: ml=−l,−(l−1),…,0,…,+(l−1),+lm_l = -l, -(l-1), \dots, 0, \dots, +(l-1), +lml​=−l,−(l−1),…,0,…,+(l−1),+l

    Since: ml=−3m_l = -3ml​=−3 this is possible only if: l≥3l \ge 3l≥3

    Also, for principal quantum number n=4n = 4n=4, the allowed values of lll are: l=0,1,2,3l = 0,1,2,3l=0,1,2,3

    Therefore, the only possible value is: l=3l = 3l=3

  3. Use the formula for radial nodes

    Number of radial nodes is given by: n−l−1n - l - 1n−l−1

    Substituting n=4n = 4n=4 and l=3l = 3l=3: 4−3−1=04 - 3 - 1 = 04−3−1=0

  4. Final answer

    The number of radial nodes is: 0\boxed{0}0​

  5. Comparison with stored answer

    Stored correct answer: 000

    Our derived answer matches the stored answer.

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