Assertion (A) : There are two spherical nodes in `3s` orbital
Reason (R ) : There is no planer nodes in `3s` orbital.

Options

A. If both (A) and (R ) correct and (R ) is the correct explanation for (A)
B. If both (A) and (R ) correct and (R ) is not the correct explanation for (A)
C. If (A) is correct but (R ) is incorrect
D. If (A) is incorrect but (R ) is correct

Explanation

To solve the assertion and reason question regarding the `3s` orbital, we will follow these steps:

### Step 1: Understand the Assertion
The assertion states that there are two spherical nodes in the `3s` orbital. To verify this, we need to use the formula for calculating the total number of nodes in an orbital.

### Step 2: Calculate Total Nodes
The total number of nodes in an orbital is given by the formula:
\[ \text{Total Nodes} = n - 1 \]
where \( n \) is the principal quantum number.

For the `3s` orbital:
- \( n = 3 \)
- Therefore, the total nodes = \( 3 - 1 = 2 \)

### Step 3: Calculate Spherical Nodes
The number of spherical nodes is given by the formula:
\[ \text{Spherical Nodes} = n - 1 - l \]
where \( l \) is the angular momentum quantum number.

For the `3s` orbital:
- \( s \) corresponds to \( l = 0 \)
- Thus, the spherical nodes = \( 3 - 1 - 0 = 2 \)

### Step 4: Conclusion for Assertion
Since we calculated that there are indeed 2 spherical nodes in the `3s` orbital, the assertion is **true**.

### Step 5: Understand the Reason
The reason states that there are no planar nodes in the `3s` orbital. To verify this, we need to calculate the angular nodes.

### Step 6: Calculate Angular Nodes
The number of angular nodes is equal to \( l \). For the `3s` orbital:
- \( l = 0 \)
- Therefore, the angular nodes = \( 0 \)

### Step 7: Conclusion for Reason
Since there are 0 angular nodes, there are also no planar nodes in the `3s` orbital. Thus, the reason is also **true**.

### Step 8: Relationship Between Assertion and Reason
While both the assertion and reason are true, the reason does not explain the assertion. The assertion talks about the number of spherical nodes, while the reason discusses planar nodes, which are not directly related.

### Final Conclusion
- Assertion (A) is true: There are two spherical nodes in the `3s` orbital.
- Reason (R) is true: There are no planar nodes in the `3s` orbital.
- However, R is not the correct explanation of A.

### Answer
The correct option is: A is true, R is true, but R is not the correct explanation of A.

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