Given below are two statements :
Statement (I) : For a given shell, the total number of allowed orbitals is given by n².
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 :

Solution

Chemistry ma’am · 4 steps

Check each statement against what n and l allow, and both hold up.

1. Statement I. In shell n, the value of l runs from 0 to n-1, and each subshell has 2l+1 orbitals. Adding these up gives the total number of orbitals in the shell.

   Σₗ₌₀ⁿ⁻¹(2l+1) = 1 + 3 + 5 + … + (2n-1) = n²

2. Quick check. For n = 3: the 3s, 3p and 3d subshells hold 1 + 3 + 5 = 9 = 3² orbitals. So Statement I is true.
3. Statement II. The magnetic quantum number mₗ gives the spatial orientation of an orbital. It takes every whole-number value from -l to +l, including zero. For a p subshell (l = 1), that gives -1, 0, +1, the three p orbitals. So Statement II is true.
4. So. Both statements are true, which is option (a).

The idea to keep. Orbitals per subshell is 2l+1, set by the mₗ values from -l to +l. Orbitals per shell is n², and electrons per shell is 2n². Keep these three counts apart.

Answer from the NTA final answer key. Solution by PrepWiser.