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Structure of Atom question

2023 · 8 Apr · Shift 2 · Q19
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Structure of Atom question

2023 · 8 Apr · Shift 2 · Q19

JEE MainChemistryStructure of AtomNumerical+4 / −1
The number of atomic orbitals from the following having 5 radial nodes is ‾\underline{\hspace{2cm}}​. 7s,7p,6s,8p,8d7 \mathrm{s}, 7 \mathrm{p}, 6 \mathrm{s}, 8 \mathrm{p}, 8 \mathrm{d}7s,7p,6s,8p,8d
Numerical answer
View written solutionFree

Correct answer: 3

  1. Use the formula for radial nodes

For an atomic orbital, the number of radial nodes is:

Radial nodes=n−l−1\text{Radial nodes} = n-l-1Radial nodes=n−l−1

where:

  • nnn = principal quantum number
  • lll = azimuthal quantum number

Also,

  • for sss orbital: l=0l=0l=0
  • for ppp orbital: l=1l=1l=1
  • for ddd orbital: l=2l=2l=2
  1. Check each given orbital

(i) 7s7s7s

Here, n=7n=7n=7, l=0l=0l=0

Radial nodes=7−0−1=6\text{Radial nodes} = 7-0-1=6Radial nodes=7−0−1=6

So, 7s7s7s does not have 5 radial nodes.

(ii) 7p7p7p

Here, n=7n=7n=7, l=1l=1l=1

Radial nodes=7−1−1=5\text{Radial nodes} = 7-1-1=5Radial nodes=7−1−1=5

So, 7p7p7p has 5 radial nodes.

(iii) 6s6s6s

Here, n=6n=6n=6, l=0l=0l=0

Radial nodes=6−0−1=5\text{Radial nodes} = 6-0-1=5Radial nodes=6−0−1=5

So, 6s6s6s has 5 radial nodes.

(iv) 8p8p8p

Here, n=8n=8n=8, l=1l=1l=1

Radial nodes=8−1−1=6\text{Radial nodes} = 8-1-1=6Radial nodes=8−1−1=6

So, 8p8p8p does not have 5 radial nodes.

(v) 8d8d8d

Here, n=8n=8n=8, l=2l=2l=2

Radial nodes=8−2−1=5\text{Radial nodes} = 8-2-1=5Radial nodes=8−2−1=5

So, 8d8d8d has 5 radial nodes.

  1. Count the orbitals satisfying the condition

The orbitals with 5 radial nodes are:

7p, 6s, 8d7p,\ 6s,\ 8d7p, 6s, 8d

Hence, the total number is:

333
  1. Comparison with stored correct answer

Stored correct answer = 333

Our derived answer = 333

So, the answer agrees with the stored correct answer.

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