What will be the sum of nodal palnes of all the orbitals available in I st shell | TestHub

Passage / Comprehension

In ALLEN's classroom, teacher explains that a set of 4 quantum number are provided to give complete information of electron. The quantum numbers are Principal quantum number (n) Azimuthal quantum number ( $ℓ$ ) Magnetic quantum number (m) Spin quantum number (s) Values of these quantum number are assigned as usual by the teacher. After that a question is asked by a student named Tom Cat "Sir, what will be happen if we change the assigned values of these quantum number, like -

$n = 1 to \infty ℓ = 0 to n m = - ℓ to + ℓ (including zero) s = + \frac{1}{2} and - \frac{1}{2}$

Try to answer Tom Cat's question on the basis of given set of quantum numbers

What will be the sum of nodal palnes of all the orbitals available in I $^{st}$ shell ?

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Solution:

For the 1ˢᵗ shell ( $n = 1$ ), the value of $ℓ$ ranges from $0$ to $n$ , which gives $ℓ = 0$ and $ℓ = 1$ . For $ℓ = 0$ , there is 1 orbital ( $m = 0$ ) with 0 nodal planes (since the number of nodal planes = $ℓ$ ). For $ℓ = 1$ , there are 3 orbitals ( $m = - 1, 0, + 1$ ), each having 1 nodal plane. The sum of all nodal planes in the 1ˢᵗ shell is $(1 \times 0) + (3 \times 1) = 3$ .

Chemistry - GENERAL CHEMISTRY Question with Solution | TestHub

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