Consider the ground state of an atom (Z = 24). How many electrons are arranged with Azimuthal quantum number $ l = 1 $ and $ l = 2 $ respectively?
Show Hint
- 12 and 4
- 16 and 4
- 12 and 5
- 12 and 5 and 6
The Correct Option is C
Approach Solution - 1
The question asks about the distribution of electrons in the ground state for an atom with atomic number \( Z = 24 \). We need to find the number of electrons with azimuthal quantum numbers \( l = 1 \) and \( l = 2 \).
First, we determine the electron configuration for chromium (\( Z = 24 \)) in its ground state:
Electron Configuration:
The electron configuration of chromium is \( 1s^2 \, 2s^2 \, 2p^6 \, 3s^2 \, 3p^6 \, 3d^5 \, 4s^1 \).
Now, we interpret the distribution of electrons for each principal energy level and their respective subshells by azimuthal quantum numbers:
- The subshell \( s \) has \( l = 0 \).
- The subshell \( p \) has \( l = 1 \).
- The subshell \( d \) has \( l = 2 \).
Next, we identify how many electrons are in subshells corresponding to each azimuthal quantum number:
**Electrons with \( l = 1 \) (p subshells):**
- \( 2p^6 \) — 6 electrons
- \( 3p^6 \) — 6 electrons
Total electrons with \( l = 1 \): \( 6 + 6 = 12 \).
Electrons with \( l = 2 \) (d subshells):
- \( 3d^5 \) — 5 electrons
Total electrons with \( l = 2 \): 5.
Therefore, the number of electrons with azimuthal quantum numbers \( l = 1 \) and \( l = 2 \) are 12 and 5, respectively.
Conclusion: The correct answer is 12 and 5.
Approach Solution -2
The problem requires determining the number of electrons in the ground state of an atom with atomic number \( Z = 24 \) (chromium), that have azimuthal quantum numbers \( l = 1 \) and \( l = 2 \). Here is the step-by-step explanation:
- The ground state electron configuration of an atom is determined by filling electrons in orbitals ranked by energy levels using the Aufbau principle. For chromium (atomic number \( Z = 24 \)), the electron configuration is:
- \( 1s^2 \) for \( n = 1, \, l = 0 \)
- \( 2s^2, \, 2p^6 \) for \( n = 2, \, l = 0, \, 1 \) (with \( 2p \) having 6 electrons, all with \( l = 1 \))
- \( 3s^2, \, 3p^6 \) for \( n = 3, \, l = 0, \, 1 \) (with \( 3p \) having 6 electrons, all with \( l = 1 \))
- \( 3d^5, \, 4s^1 \) for \( n = 3, \, 4 , \, l = 2, \, 0 \) (with \( 3d \) having 5 electrons, all with \( l = 2 \))
- Identify the electrons with azimuthal quantum number \( l = 1 \):
- The electrons in \( 2p \) orbitals: 6 electrons for \( n = 2, \, l = 1 \).
- The electrons in \( 3p \) orbitals: 6 electrons for \( n = 3, \, l = 1 \).
- Identify the electrons with azimuthal quantum number \( l = 2 \):
- The electrons in \( 3d \) orbitals: 5 electrons for \( n = 3, \, l = 2 \).
- Hence, the number of electrons arranged with azimuthal quantum numbers \( l = 1 \) and \( l = 2 \) are respectively 12 and 5.
Therefore, the correct answer is: 12 and 5.
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