The radial probability is the probability of finding electron in a small spherical shell around the nucleus at a particular distance r. Hence radial probability is

Options

A. `4pi r^(2) dr Psi^(2)`
B. `(4//3) pi r^(2) dr Psi^(2)`
C. `2pi r^(2) dr Psi^(2)`
D. `4pi r dr Psi`

Explanation

To derive the expression for radial probability, we will follow these steps:

### Step 1: Understanding Radial Probability
The radial probability refers to the likelihood of finding an electron in a small spherical shell at a distance \( r \) from the nucleus. This concept is essential in quantum mechanics, particularly in the study of atomic structure.

### Step 2: Wave Function and Probability
The probability of finding an electron at a specific point in space is determined by the square of the wave function \( \Psi \). Therefore, the probability \( P \) of finding the electron in a small volume element \( dV \) is given by:
\[
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