The number of nodes possible in radial probability distribution curve of 3d orbital is

Options

A. 1
B. 2
C. 3
D. 0

Answer

To determine the number of nodes in the radial probability distribution curve of a 3d orbital, we can follow these steps:

### Step 1: Understand the concept of nodes
Nodes are points in an orbital where the probability of finding an electron is zero. In quantum mechanics, there are two types of nodes: angular nodes and radial nodes. For this question, we are specifically interested in radial nodes.

### Step 2: Identify the quantum numbers for the 3d orbital
The 3d orbital has two quantum numbers:
- Principal quantum number (n): For the 3d orbital, n = 3.
- Azimuthal quantum number (l): For the d orbitals, l = 2.

### Step 3: Use the formula for calculating radial nodes
The number of radial nodes can be calculated using the formula:
\[ \text{Number of radial nodes} = n - l - 1 \]

### Step 4: Substitute the values into the formula
Now, we substitute the values of n and l into the formula:
- n = 3
- l = 2

So, we calculate:
\[ \text{Number of radial nodes} = 3 - 2 - 1 \]
\[ \text{Number of radial nodes} = 3 - 3 \]
\[ \text{Number of radial nodes} = 0 \]

### Step 5: Conclusion
The number of radial nodes in the radial probability distribution curve of the 3d orbital is 0.

### Final Answer:
The correct answer is 0.

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