Radial Probability and Radial Probability Density

1. Radial Probability

Radial probability refers to the probability of finding an electron within a spherical shell of radius r and thickness dr around the nucleus.

• It depends on the distance of the electron from the nucleus.
• It is represented by P(r).
• It is obtained by multiplying the probability density by the volume of the spherical shell.
• The radial probability is maximum at the most probable distance from the nucleus.

Formula:

P(r) dr = 4πr² |ψ|² dr

2. Radial Probability Density

Radial probability density represents the probability of finding an electron per unit volume at a particular distance from the nucleus.

• It depends on the square of the radial wave function.
• It is represented by |ψ|² for a spherically symmetric orbital.
• It does not include the volume factor 4πr².
• It is maximum where the probability density is highest.

Formula:

Radial probability density = |ψ|²

Difference Between Radial Probability and Radial Probability Density

Radial Probability	Radial Probability Density
Probability of finding an electron in a spherical shell of thickness dr.	Probability density at a particular point in space.
Includes the volume factor 4πr².	Does not include the volume factor 4πr².
Depends on both distance and wave function.	Depends on the square of the wave function.
Represented by P(r)dr.	Represented by	ψ	² for spherically symmetric orbitals.