• brainyman89
In summary, the radial probability density (RPD) is equal to the square of the radial wavefunction multiplied by the volume of the spherical shell. In order to simplify the equation, the dr term was cancelled out, as it represents the derivative of the distribution. The derivative with respect to r is represented by the density function R(r). Therefore, the entire wave function does not need to be multiplied by the volume, only the radial probability component.
brainyman89
The required volume is determined by the volume of the SPHERICAL SHELL enclosed between a sphere of radius (r+dr) and a sphere of radius r

rpd = radial probability density × volume of the spherical shell = R2 × 4πr2 drhow then did they cancel the dr and directly write:
rpd = R2 × 4πr2

??

also how could only radial probability be multiplied by volume? shouldn't the whole wave function be multiplied by the volume?

Last edited:
The density function is the derivative of the distribution - that's where the dr went.

mathman said:
The density function is the derivative of the distribution - that's where the dr went.

derivative with respect to what?

brainyman89 said:
derivative with respect to what?

The cumulative distribution is F(r) and the density function R(r) = dF(r)/dr

## 1. What is radial probability distribution?

Radial probability distribution (RPD) is a mathematical function that describes the probability of finding an electron at a certain distance from the nucleus in an atom. It is represented graphically as a plot of the probability density against the distance from the nucleus.

## 2. How is radial probability distribution calculated?

The radial probability distribution is calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics. It involves solving a complex mathematical equation using numerical methods or analytical approximations.

## 3. What does the shape of an RPD graph indicate?

The shape of an RPD graph indicates the probability of finding an electron at a certain distance from the nucleus. The higher the peak of the graph, the higher the probability of finding an electron at that distance.

## 4. What is the significance of RPD in understanding the electron behavior in atoms?

RPD is significant in understanding the electron behavior in atoms because it provides insight into the distribution of electrons around the nucleus. It helps to explain the stability of atoms and the arrangement of electrons in different energy levels.

## 5. How does RPD differ from electron density?

RPD and electron density are related but not the same. RPD is a probability distribution that describes the likelihood of finding an electron at a certain distance from the nucleus. Electron density, on the other hand, is a measure of the number of electrons in a given volume of space. RPD takes into account the probability of finding an electron at a certain distance, while electron density does not consider the probability factor.

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