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Structure of Atom question

2016 · 9 Apr · Shift 1 · Q18
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Structure of Atom question

2016 · 9 Apr · Shift 1 · Q18

JEE MainChemistryStructure of AtomMCQ+4 / −1
The total number of orbitals associated with the principal quantum number 5 is :
  1. A
    5
  2. B
    10
  3. C
    20
  4. D
    25
View written solutionFree

Correct answer: D

  1. For a given principal quantum number nnn, the allowed values of azimuthal quantum number lll are: l=0,1,2,…,(n−1)l=0,1,2,\dots,(n-1)l=0,1,2,…,(n−1)

  2. For each value of lll, the number of orbitals is: 2l+12l+12l+1

  3. Therefore, the total number of orbitals in the shell with principal quantum number nnn is: ∑l=0n−1(2l+1)=n2\sum_{l=0}^{n-1}(2l+1)=n^2∑l=0n−1​(2l+1)=n2

  4. Here, n=5n=5n=5. So, Total orbitals=52=25\text{Total orbitals}=5^2=25Total orbitals=52=25

  5. Hence, the correct option is: D: 25\boxed{\text{D: }25}D: 25​

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