Which orbital has only positive value of wave function at all distances from the nucleus :
(a)1s
(b)2s
(c)3p
(d)3d

Options

A. 1s
B. 2s
C. 3p
D. 3d

Answer

To determine which orbital has only positive values of the wave function at all distances from the nucleus, we can analyze the given options based on the properties of wave functions and nodes.

### Step-by-Step Solution:

1. **Understanding Wave Functions**:
- The wave function (ψ) describes the probability amplitude of finding an electron in a given region of space. For an orbital to have only positive values of the wave function, it should not cross zero at any point (i.e., it should not have any nodes).

2. **Identifying Radial Nodes**:
- Radial nodes occur where the wave function equals zero. The number of radial nodes can be calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]
where \( n \) is the principal quantum number and \( l \) is the azimuthal quantum number.

3. **Analyzing Each Option**:
- **(a) 1s**:
- For 1s: \( n = 1 \), \( l = 0 \)
- Radial nodes = \( 1 - 0 - 1 = 0 \) (No nodes, only positive values)
- **(b) 2s**:
- For 2s: \( n = 2 \), \( l = 0 \)
- Radial nodes = \( 2 - 0 - 1 = 1 \) (One node, not all positive)
- **(c) 3p**:
- For 3p: \( n = 3 \), \( l = 1 \)
- Radial nodes = \( 3 - 1 - 1 = 1 \) (One node, not all positive)
- **(d) 3d**:
- For 3d: \( n = 3 \), \( l = 2 \)
- Radial nodes = \( 3 - 2 - 1 = 0 \) (No nodes, but 3d orbitals have angular nodes)

4. **Conclusion**:
- The only orbital that has no nodes and thus only positive values of the wave function at all distances from the nucleus is the **1s orbital**.

### Final Answer:
**(a) 1s**