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The following quantum numbers are possib...

The following quantum numbers are possible for how many orbitals `(s) n = 3, l = 2, m = + 2` ?

A

1

B

2

C

3

D

4

Text Solution

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The correct Answer is:
To determine how many orbitals are possible with the given quantum numbers \( n = 3 \), \( l = 2 \), and \( m = +2 \), we can follow these steps: ### Step 1: Identify the Principal Quantum Number (n) The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 3 \) means we are looking at the third energy level. **Hint:** The principal quantum number \( n \) can take positive integer values (1, 2, 3, ...). ### Step 2: Identify the Azimuthal Quantum Number (l) The azimuthal quantum number \( l \) determines the shape of the orbital and is related to the subshell. The value of \( l \) can range from \( 0 \) to \( n-1 \). For \( l = 2 \): - \( l = 0 \) corresponds to an s subshell - \( l = 1 \) corresponds to a p subshell - \( l = 2 \) corresponds to a d subshell Since \( l = 2 \), we are dealing with a d subshell. **Hint:** The azimuthal quantum number \( l \) indicates the type of subshell: 0 (s), 1 (p), 2 (d), 3 (f). ### Step 3: Identify the Magnetic Quantum Number (m) The magnetic quantum number \( m \) can take integer values ranging from \( -l \) to \( +l \). For \( l = 2 \), \( m \) can take the values: - \( m = -2 \) - \( m = -1 \) - \( m = 0 \) - \( m = +1 \) - \( m = +2 \) This gives us a total of 5 possible values for \( m \), which correspond to 5 different orbitals in the d subshell. **Hint:** The magnetic quantum number \( m \) specifies the orientation of the orbital and can take values from \( -l \) to \( +l \). ### Step 4: Determine the Number of Orbitals for Given m In this case, \( m = +2 \) is one specific value of the magnetic quantum number. Each value of \( m \) corresponds to one unique orbital. Therefore, if \( m \) is specified as \( +2 \), it indicates that we are referring to one specific orbital within the 3d subshell. **Hint:** Each specific value of \( m \) corresponds to one orbital. ### Conclusion Thus, for the quantum numbers \( n = 3 \), \( l = 2 \), and \( m = +2 \), there is only **1 orbital** that corresponds to these quantum numbers. **Final Answer:** 1 orbital
To determine how many orbitals are possible with the given quantum numbers \( n = 3 \), \( l = 2 \), and \( m = +2 \), we can follow these steps: ### Step 1: Identify the Principal Quantum Number (n) The principal quantum number \( n \) indicates the energy level of the electron. Here, \( n = 3 \) means we are looking at the third energy level. **Hint:** The principal quantum number \( n \) can take positive integer values (1, 2, 3, ...). ### Step 2: Identify the Azimuthal Quantum Number (l) ...
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