Given below are two statements : Statement (I) : For a given shell, the total number of allowed orbitals is given by n^2 . Statement (II) : For any subshell, the spatial orientation of the orbitals is given by -l to +l values including zero. In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are false

Statement I is false but Statement II is true

Statement I is true but Statement II is false

Structure of Atom PYQ — JEE Main 2025 · 23 Jan · Shift 2 · Q16 with Solution

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Correct answer: A

For a shell with principal quantum number $n$ , the allowed subshells have values of $l$ from: $l=0 \, \text{to} \, n-1$

For each value of $l$ , the number of orbitals in that subshell is: $2l+1$

So, total number of orbitals in the shell is: $\sum_{l=0}^{n-1}(2l+1)$

This sum equals: $1+3+5+\cdots +(2n-1)=n^2$

Hence, Statement (I) is true.

For a given subshell with azimuthal quantum number $l$ , the magnetic quantum number $m_l$ determines the spatial orientation of orbitals.

Its possible values are: $m_l=-l, -(l-1), \dots, -1, 0, 1, \dots, (l-1), l$

So the values run from $-l$ to $+l$ , including zero.

Hence, Statement (II) is also true.

Both Statement (I) and Statement (II) are true.

Therefore, the correct option is: $\boxed{\text{A}}$

Stored correct answer: A

My derived answer: A

So, the derived answer agrees with the stored correct answer.