Which one of the following expressions represent the electron probability function (D)

Options

A. `4pi r dr psi^(2)`
B. `4pi r^(2) dr psi`
C. `4pi r^(2) dr psi^(2)`
D. `4pi r dr psi`

Answer

To solve the question regarding which expression represents the electron probability function (D), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Electron Probability Function**:
- The electron probability function refers to the likelihood of finding an electron in a particular region around the nucleus of an atom. This is often expressed in terms of a wave function (ψ).

2. **Identify the Components of the Probability Function**:
- The probability of finding an electron in a small volume is given by the expression:
\[ D = 4\pi r^2 \, dr \, |\psi|^2 \]
- Here, \(4\pi r^2\) represents the surface area of a sphere with radius \(r\), \(dr\) is a small change in radius (a small volume element), and \(|\psi|^2\) is the probability density function derived from the wave function.

3. **Examine the Given Options**:
- We need to evaluate the options provided to determine which one matches the expression for the electron probability function.
- The correct expression must include \(4\pi r^2\), \(dr\), and \(|\psi|^2\).

4. **Evaluate Each Option**:
- Option 1: \(4\pi r \, dr \, \psi^2\) - This is incorrect because it lacks \(r^2\).
- Option 2: \(4\pi r^2 \, dr \, \psi\) - This is incorrect because it lacks \(|\psi|^2\).
- Option 3: \(4\pi r^2 \, dr \, |\psi|^2\) - This is correct as it includes all necessary components.
- Option 4: \(4\pi r \, dr \, \psi\) - This is incorrect for the same reason as option 1.

5. **Conclusion**:
- The correct expression that represents the electron probability function (D) is:
\[ D = 4\pi r^2 \, dr \, |\psi|^2 \]