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Structure of Atom question

2022 · 27 Jun · Shift 2 · Q16
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Structure of Atom question

2022 · 27 Jun · Shift 2 · Q16

JEE MainChemistryStructure of AtomNumerical+4 / −1

Consider the following set of quantum numbers.

n 1 m 1_11​
A. 3 3 −-− 3
B. 3 2 −-− 2
C. 2 1 +1
D. 2 2 +2

The number of correct sets of quantum numbers is ‾\underline{\hspace{2cm}}​.

Numerical answer
View written solutionFree

Correct answer: 2

  1. For a valid set of quantum numbers, the following rules must hold:

    • Principal quantum number: n=1,2,3,…n = 1,2,3,\dotsn=1,2,3,…
    • Azimuthal quantum number: l=0,1,2,…,(n−1)l = 0,1,2,\dots,(n-1)l=0,1,2,…,(n−1)
    • Magnetic quantum number: 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

  2. Now check each given set:

    A. n=3, l=3, ml=−3n=3,\ l=3,\ m_l=-3n=3, l=3, ml​=−3

    • For n=3n=3n=3, allowed values of lll are 0,1,20,1,20,1,2.
    • Here l=3l=3l=3, which is not allowed.
    • So, A is incorrect.

    B. n=3, l=2, ml=−2n=3,\ l=2,\ m_l=-2n=3, l=2, ml​=−2

    • For n=3n=3n=3, allowed values of lll are 0,1,20,1,20,1,2.
    • So l=2l=2l=2 is allowed.
    • For l=2l=2l=2, allowed mlm_lml​ values are −2,−1,0,+1,+2-2,-1,0,+1,+2−2,−1,0,+1,+2.
    • Here ml=−2m_l=-2ml​=−2, which is allowed.
    • So, B is correct.

    C. n=2, l=1, ml=+1n=2,\ l=1,\ m_l=+1n=2, l=1, ml​=+1

    • For n=2n=2n=2, allowed values of lll are 0,10,10,1.
    • So l=1l=1l=1 is allowed.
    • For l=1l=1l=1, allowed mlm_lml​ values are −1,0,+1-1,0,+1−1,0,+1.
    • Here ml=+1m_l=+1ml​=+1, which is allowed.
    • So, C is correct.

    D. n=2, l=2, ml=+2n=2,\ l=2,\ m_l=+2n=2, l=2, ml​=+2

    • For n=2n=2n=2, allowed values of lll are 0,10,10,1.
    • Here l=2l=2l=2, which is not allowed.
    • So, D is incorrect.

  3. Therefore, the correct sets are B and C.

  4. Hence, the number of correct sets is

222

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