Question

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:

• A. Statement I is true but Statement II is false
• B. Statement I is false but Statement II is true
• C. Both Statement I and Statement II are true
• D. Both Statement I and Statement II are false

Hint:

For any shell with quantum number \( n \), the total number of orbitals is \( n^2 \). For a subshell with quantum number \( l \), the possible values for the magnetic quantum number \( m_l \) range from \( -l \) to \( +l \), including zero.

Answer 1

The Correct Option is C

Statement (I): For a given shell with principal quantum number \( n \), the total number of orbitals is indeed \( n^2 \), as each subshell (s, p, d, f) has \( l \) values, and the number of orbitals per subshell is \( 2l + 1 \). Therefore, the total number of orbitals for a shell is \( n^2 \).
- Statement (II): For any subshell with angular momentum quantum number \( l \), the spatial orientations of the orbitals are given by values from \( -l \) to \( +l \) including zero, which is also true. Thus, both statements are true.