Assertion. The plots of probability density and radial probability function versus distance r from the nucleus for any particular orbital are not identical
Reason. Probability density is `Psi^(2)` whereas radial probability function represents probability of finding the electron in a shell of thickness `dr`.

Options

A. If both assertion and reason are true, and reason is the true explanation of the assertion
B. If both assertion and reason are true, but reason is not the true explanation of the assertion
C. If assertion is true, but reason is false
D. If both assertion and reason are false

Explanation

To solve the question, we need to analyze the assertion and reason provided:

**Assertion:** The plots of probability density and radial probability function versus distance \( r \) from the nucleus for any particular orbital are not identical.

**Reason:** Probability density is \( \Psi^2 \) whereas radial probability function represents the probability of finding the electron in a shell of thickness \( dr \).

### Step-by-Step Solution:

1. **Understanding Probability Density:**
- Probability density for an electron in an orbital is given by the square of the wave function, \( \Psi^2 \). This function describes the likelihood of finding an electron at a specific point in space.
- The plot of \( \Psi^2 \) versus distance \( r \) from the nucleus shows how the probability density changes with distance.

**Hint:** Remember that \( \Psi^2 \) gives the probability density at a point in space.

2. **Understanding Radial Probability Function:**
- The radial probability function, on the other hand, is defined as \( 4\pi r^2 \Psi^2 \). This function accounts for the volume element in spherical coordinates, which is important because electrons can be found in any direction around the nucleus.
- The radial probability function represents the probability of finding an electron within a spherical shell of thickness \( dr \) at a distance \( r \) from the nucleus.

**Hint:** The radial probability function incorporates the geometry of space, which is why it includes the factor \( 4\pi r^2 \).

3. **Comparing the Two Functions:**
- When we plot both \( \Psi^2 \) and \( 4\pi r^2 \Psi^2 \) against \( r \), we will see that the shapes of these plots are different. The probability density plot shows how likely it is to find an electron at a specific point, while the radial probability function shows how likely it is to find the electron within a spherical shell.
- Therefore, the assertion that these plots are not identical is correct.

**Hint:** Visualize the graphs: one is a function of distance, while the other is a function of the volume around that distance.

4. **Evaluating the Reason:**
- The reason provided states that probability density is \( \Psi^2 \) and that the radial probability function represents the probability of finding the electron in a shell of thickness \( dr \). This statement is accurate and correctly explains why the two plots differ.
- Thus, the reason supports the assertion.

**Hint:** Check if the reason logically follows from the assertion.

5. **Conclusion:**
- Both the assertion and the reason are true, and the reason correctly explains the assertion. Therefore, the correct answer is that both the assertion and reason are true, and the reason is the correct explanation for the assertion.

**Final Answer:** Both the assertion and reason are true, and the reason is the correct explanation for the assertion.