The orbital having zero probability of finding electron on the surface of nucleus is

Options

A. s
B. `p_(x)`
C. `d_(x^(2) -y^(2))`
D. Both (2)& (3)

Answer

To solve the question regarding which orbital has zero probability of finding an electron at the surface of the nucleus, we will analyze the given options step by step.

### Step 1: Understand the Orbitals
We have three types of orbitals to consider:
- **s orbital**
- **px orbital**
- **dx² - y² orbital**

### Step 2: Analyze the s Orbital
The **s orbital** has a spherical shape, with the nucleus at the center. The probability of finding an electron is distributed evenly throughout the sphere. Therefore, there is a non-zero probability of finding an electron at the nucleus.

**Conclusion for s orbital**: There is a probability of finding an electron at the nucleus, so it does not have zero probability.

### Step 3: Analyze the px Orbital
The **px orbital** has a dumbbell shape, with two lobes extending along the x-axis. The center of the px orbital (where the nucleus is located) is a node, meaning there is zero probability of finding an electron at that point.

**Conclusion for px orbital**: There is zero probability of finding an electron at the nucleus.

### Step 4: Analyze the dx² - y² Orbital
The **dx² - y² orbital** also has a shape that resembles a double dumbbell, with lobes extending along the x and y axes. Similar to the px orbital, the center of this orbital (where the nucleus is located) is also a node, indicating that there is zero probability of finding an electron at that point.

**Conclusion for dx² - y² orbital**: There is zero probability of finding an electron at the nucleus.

### Step 5: Final Conclusion
From the analysis:
- The **s orbital** has a non-zero probability at the nucleus.
- The **px orbital** has zero probability at the nucleus.
- The **dx² - y² orbital** also has zero probability at the nucleus.

Thus, the correct answer is option **D**: both the **px orbital** and the **dx² - y² orbital** have zero probability of finding an electron at the surface of the nucleus.

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