In the Zn2+ ion (in its ground state), how many electrons are l = 0 and s = -1/2? The atomic number of Zn is 30.
The correct answer and explanation is:
Correct Answer: 5 electrons
Explanation:
To solve this question, we need to understand the electronic configuration of the Zn²⁺ ion and identify the electrons that have azimuthal quantum number (l) = 0 and spin quantum number (s) = -1/2.
Step 1: Atomic Number and Neutral Zinc Configuration
Zinc has an atomic number of 30, which means a neutral zinc atom has 30 electrons. The electron configuration of neutral Zn is:
Zn: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s²
Step 2: Zinc Ion Zn²⁺ Configuration
The Zn²⁺ ion has lost two electrons. Electrons are always removed from the outermost shell first, which means from the 4s orbital.
So, Zn²⁺ configuration becomes:
Zn²⁺: 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰
Now Zn²⁺ has 28 electrons.
Step 3: Determine How Many Electrons Have l = 0 and s = -1/2
- The l = 0 quantum number corresponds to s orbitals.
- The s = -1/2 refers to electrons with spin down.
Now count the electrons in s-orbitals (l = 0):
- 1s² → 1 electron with s = -1/2
- 2s² → 1 electron with s = -1/2
- 3s² → 1 electron with s = -1/2
Each s orbital holds 2 electrons, one with spin +1/2 and one with spin -1/2.
There are three s-orbitals, and each has one electron with spin -1/2:
1s² → 1
2s² → 1
3s² → 1
In addition, 4s² would have had 1 more, but those were removed in forming Zn²⁺.
So far, this gives 3 electrons.
However, we missed the s electrons in the p shells:
- 2p⁶: electrons are not s-type (l = 1)
- 3p⁶: same
Now reconsider: are there other s-type electrons? Yes, 4s² originally had 2, but those were removed.
So the only s orbitals with electrons are:
- 1s²
- 2s²
- 3s²
Each contributes 1 spin-down electron.
Therefore, the number of electrons with l = 0 and s = -1/2 in Zn²⁺ is 3.
Correction: this shows 3, not 5.
Let us now double-check and correct accordingly.
Final Confirmation:
Electrons in s-orbitals in Zn²⁺:
- 1s²: 1 spin-down
- 2s²: 1 spin-down
- 3s²: 1 spin-down
That gives 3 electrons.
Therefore, the correct answer is: 3 electrons