The value of magnetic quantum number of the outermost electron of Zn+ ion is ......... .

Q: Why do we remove the electron from the $4s$ orbital instead of the $3d$ orbital?

Even though the $3d$ orbital is filled after the $4s$ orbital according to the $n+l$ rule, the $4s$ orbital is physically further from the nucleus (higher principal quantum number $n=4$). Therefore, it experiences less effective nuclear charge and its electrons are removed first during ionization.

Q: What is the difference between the azimuthal and magnetic quantum numbers?

The azimuthal quantum number ($l$) determines the shape of the orbital (s, p, d, f), while the magnetic quantum number ($m$) determines the spatial orientation of that orbital along the x, y, and z axes.

Q: Can the magnetic quantum number ever be negative for an $s$-orbital?

No. The magnetic quantum number $m$ ranges from $-l$ to $+l$. Since an $s$-orbital always has $l=0$, the only possible value for $m$ is $0$.

Q: What if the question asked for the $\text{Zn}^{2+}$ ion?

For the $\text{Zn}^{2+}$ ion, we would remove both electrons from the $4s$ orbital. The outermost electrons would then be in the $3d$ subshell, which has $l=2$, meaning $m$ could be $-2, -1, 0, +1, \text{ or } +2$.

Q: Is the $4s$ electron paired or unpaired in the $\text{Zn}^+$ ion?

Since the neutral Zinc atom has a $4s^2$ configuration (paired), removing one electron leaves a $4s^1$ configuration. Thus, the outermost electron in $\text{Zn}^+$ is unpaired.

Question

The value of magnetic quantum number of the outermost electron of $	ext{Zn}^+$ ion is ......... .

Sigma Percentile · Accepted Answer

### The Quantum Address of an Electron
Every electron in an atom has a unique "address" defined by four quantum numbers. These numbers describe the energy, shape, orientation, and spin of the electron's orbital. Understanding these numbers is like having a GPS for the subatomic world.

### Decoding the Zinc Atom
Zinc, with an atomic number of $Z = 30$, is a fascinating transition metal. To understand its chemistry, we must first build its electronic configuration from the ground up. Following the Aufbau principle, electrons fill lower energy orbitals first. The ground state configuration of a neutral Zinc atom is $[	ext{Ar}] 3d^{10} 4s^2$.

### The Catch: Forming the Cation
When a transition metal like Zinc loses an electron to form a cation, a common pitfall awaits many students. One might assume that the last electron added (in the $3d$ subshell) is the first to leave. However, this is not the case! Electrons are always removed from the outermost principal quantum shell first. Since $n=4$ is higher than $n=3$, the electrons in the $4s$ orbital are the first to go.

Therefore, to form the $	ext{Zn}^+$ ion, we remove exactly one electron from the $4s$ orbital, leaving us with the configuration $[	ext{Ar}] 3d^{10} 4s^1$.

### Zeroing in on the Outermost Electron
With the configuration of $	ext{Zn}^+$ established, our focus shifts entirely to the lone electron in the $4s$ orbital. This is the "outermost" electron the question is asking about.

### The Final Calculation
The azimuthal quantum number, $l$, dictates the shape of the orbital. For any $s$-orbital, regardless of its principal quantum number, $l = 0$, indicating a perfectly spherical shape.

The magnetic quantum number, $m$, describes the spatial orientation of this shape and can take any integer value from $-l$ to $+l$. Since our azimuthal quantum number $l$ is $0$, the math becomes incredibly simple. The only possible value for $m$ is $0$.

**Final Answer:** The magnetic quantum number of the outermost electron of the $	ext{Zn}^+$ ion is **$0$**.

Animated Solution for Chemistry - Atomic Structure: The value of magnetic quantum number of the outermost electron of $Zn^{+}$ ion is ......... .

Enter Numerical Value:

Visualized Solution

\text{Electronic Configuration of Zn}

\text{Electronic Configuration of Zn}^+

\text{Outermost Electron}

\text{Azimuthal Quantum Number } (l)

\text{Magnetic Quantum Number } (m)

\text{Conclusion}

The Sigma Insight: Quantum Mechanical Model

The Quantum Address of an Electron Every electron in an atom has a unique "address" defined by four quantum numbers

Decoding the Zinc Atom Zinc, with an atomic number of $Z = 30$ , is a fascinating transition metal

The Catch

Zeroing in on the Outermost Electron With the configuration of $Zn^{+}$ established, our focus shifts entirely to the lone electron in the $4 s$ orbital

The Final Calculation The azimuthal quantum number, $l$ , dictates the shape of the orbital

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Animated Solution for Chemistry - Atomic Structure: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of magnetic quantum number of the outermost electron of Zn+ ion is ......... .