An electron jumps to higher excited state of a orbital which is non directional and have 4 radial node then shell with which electron belong?

Answer

To determine the shell to which the electron belongs, we need to analyze the information given in the question step by step.

### Step 1: Identify the type of orbital
The question states that the electron jumps to a higher excited state of an orbital that is non-directional. Non-directional orbitals are characteristic of **s orbitals**.

**Hint:** Remember that s orbitals are spherical and do not have a specific direction, unlike p, d, or f orbitals.

### Step 2: Determine the azimuthal quantum number (l)
For s orbitals, the azimuthal quantum number (l) is always **0**.

**Hint:** Recall the quantum numbers: for s orbitals, l = 0; for p orbitals, l = 1; for d orbitals, l = 2, and so on.

### Step 3: Use the formula for radial nodes
The problem states that there are **4 radial nodes**. The formula to calculate the number of radial nodes is:

\[ \text{Radial Nodes} = n - l - 1 \]

Where:
- n = principal quantum number (shell number)
- l = azimuthal quantum number

### Step 4: Substitute known values into the formula
We know:
- Radial nodes = 4
- l = 0 (since it's an s orbital)

Substituting these values into the formula gives:

\[ 4 = n - 0 - 1 \]

### Step 5: Solve for n
Now, we can solve for n:

\[ 4 = n - 1 \]

Adding 1 to both sides:

\[ n = 4 + 1 \]
\[ n = 5 \]

### Step 6: Conclusion
The electron belongs to the **5th shell**.

**Final Answer:** The electron belongs to the 5th shell.

---