Element having `(4,0,0+1//2)` as a set of four quantum numbers for its valence electron is-

Options

A. `Na`
B. `Ca`
C. `K`
D. `Br`

Answer

To determine the element that has the set of quantum numbers (4, 0, 0, +1/2) for its valence electron, we need to analyze each quantum number step by step.

### Step 1: Identify the Principal Quantum Number (n)
The first quantum number is **n = 4**. This indicates that the electron is in the fourth energy level or shell.

**Hint:** The principal quantum number (n) indicates the energy level of the electron and can take positive integer values (1, 2, 3, ...).

### Step 2: Identify the Azimuthal Quantum Number (l)
The second quantum number is **l = 0**. The azimuthal quantum number (l) defines the shape of the orbital. When l = 0, it corresponds to an **s orbital**.

**Hint:** The azimuthal quantum number (l) can take values from 0 to (n-1). For l = 0, the orbital is an s orbital.

### Step 3: Identify the Magnetic Quantum Number (m)
The third quantum number is **m = 0**. The magnetic quantum number (m) specifies the orientation of the orbital. For an s orbital (where l = 0), there is only one orientation, which is m = 0.

**Hint:** The magnetic quantum number (m) can range from -l to +l. For l = 0, m can only be 0.

### Step 4: Identify the Spin Quantum Number (s)
The fourth quantum number is **s = +1/2**. The spin quantum number indicates the spin of the electron. A value of +1/2 means the electron is in an "up" spin state.

**Hint:** The spin quantum number can be either +1/2 (up spin) or -1/2 (down spin).

### Step 5: Determine the Element
Now that we have analyzed the quantum numbers:
- n = 4 indicates the fourth energy level.
- l = 0 indicates an s orbital.
- m = 0 confirms it is the only orientation of the s orbital.
- s = +1/2 indicates the electron is in an up spin state.

The electron configuration that corresponds to these quantum numbers is **4s¹**. The element with this configuration is **Potassium (K)**, which has an atomic number of 19.

### Final Answer
The element having the quantum numbers (4, 0, 0, +1/2) for its valence electron is **Potassium (K)**.

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