A `4pir^(2)Psi^(2)(r) vs" " r ` is ploted for H-orbital curve contains '3'maxima . If orbital contains 2 angular node then orbital is

Options

A. 5d
B. 4d
C. 5p
D. 4p

Explanation

To solve the problem, we need to analyze the information given about the hydrogen orbital curve and the properties of atomic orbitals. Here’s the step-by-step solution:

### Step 1: Understand the given information
We are given that the plot of \(4\pi r^2 \Psi^2(r)\) vs. \(r\) for a hydrogen orbital has 3 maxima. This indicates that there are certain radial nodes in the orbital.

### Step 2: Identify the relationship between maxima and quantum numbers
The number of maxima in the radial distribution function is related to the principal quantum number \(N\) and the angular momentum quantum number \(L\). The relationship can be expressed as:
\[ \text{Number of maxima} = N - L \]
From the problem, we know that there are 3 maxima.

### Step 3: Identify the number of angular nodes
The problem states that the orbital contains 2 angular nodes. The number of angular nodes is equal to the value of \(L\). Therefore:
\[ L = 2 \]

### Step 4: Substitute the values into the equation
Now we can substitute the known values into the equation:
\[ 3 = N - 2 \]
Solving for \(N\):
\[ N = 3 + 2 = 5 \]

### Step 5: Determine the type of orbital
The value of \(L\) corresponds to the type of orbital:
- \(L = 0\) corresponds to an s orbital
- \(L = 1\) corresponds to a p orbital
- \(L = 2\) corresponds to a d orbital
- \(L = 3\) corresponds to an f orbital

Since \(L = 2\), the orbital is a d orbital.

### Step 6: Combine the principal quantum number and angular momentum quantum number
Since we found \(N = 5\) and \(L = 2\), the orbital is designated as:
\[ 5d \]

### Final Answer
The orbital with 2 angular nodes and 3 maxima is the **5d orbital**.

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