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

To address the question, let's examine each statement independently:

1. Statement I: "The total count of permitted orbitals for a specific shell is determined by \(n^2\)."

Within atomic structure, the principal quantum number \(n\) governs the number of orbitals in a shell. The total number of orbitals for any given shell is indeed calculated as \(n^2\). Each orbital has a capacity of up to two electrons. Consequently, Statement I is accurate.

1. Statement II: "The spatial orientation of orbitals within any subshell is defined by values from \(-l\) to \(+l\), inclusive of zero."

The azimuthal quantum number \(l\) characterizes the subshell. For any given value of \(l\), the magnetic quantum number \(m_l\) dictates the spatial orientation and can adopt integer values ranging from \(-l\) to \(+l\), with zero being included. Therefore, Statement II is also accurate.

Given that both statements are factually correct according to the quantum mechanical model of the atom, the correct conclusion is:

• Both Statement I and Statement II are true