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:
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:
Show Hint
- Statement I is true but Statement II is false
- Statement I is false but Statement II is true
- Both Statement I and Statement II are true
- Both Statement I and Statement II are false
The Correct Option is C
Approach Solution - 1
To solve the question, let us analyze each statement individually:
- 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.
- 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
Approach Solution -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.
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