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 solve the question, let us analyze each statement individually: 

1. Statement I: "For a given shell, the total number of allowed orbitals is given by \(n^2\)."

In atomic structure, the number of orbitals in a shell is determined by the principal quantum number \(n\). The total number of orbitals for a given shell is indeed calculated by \(n^2\). Each orbital can hold a maximum of two electrons. Therefore, Statement I is correct.

1. Statement II: "For any subshell, the spatial orientation of the orbitals is given by \(-l\) to \(+l\) values including zero."

The azimuthal quantum number \(l\) defines the subshell. For a given value of \(l\), the magnetic quantum number \(m_l\) determines the spatial orientation and can take integer values ranging from \(-l\) to \(+l\), including zero. Thus, Statement II is also correct.

Since both statements are accurate based on the quantum mechanical model of the atom, the correct answer is:

• Both Statement I and Statement II are true

Answer 2

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.