Question

Which one of the following expressions represent the electron probability function (D)?
A). $ 4\pi rdr{\psi ^2} $
B). $ 4\pi {r^2}dr\psi $
C). $ 4\pi {r^2}dr{\psi ^2} $
D). $ 4\pi rdr\psi $

Answer 1

Hint: According to quantum mechanics, due to the probability of an electron being at a particular place cannot be predicted by uncertainty principle, such that electrons in atoms and molecules are "dispersed" in space. The electron density is proportional to the square of wave function at any location for one-electron systems.

Complete Step By Step Answer:
Since it is possible that the plot of $ {\psi ^2} $ versus distance from the nucleus (r) indicates the probability of an electron in a certain volume of space (such as a cubic Picometer) is the plot of the probability density. The 1s orbital is spherically symmetrical, therefore it depends only on its distances from the nucleus to discover a 1s electron at any given position. At r = 0 (at the nucleus) the probability density is higher and falls slowly as the distance is greater. The probability of electron density is very minimal for very large values of r, but not zero.
It also explains a method for estimating an electron's probability at a certain location. This computation generates a quantity called an electron density, which indicates that an electron may be found in a certain region at a certain place.
Correct answer is option C ( $ 4\pi {r^2}dr{\psi ^2} $ ).

Note:
Electron density or electronic density are measurements of the probability that an electron is present at an infinite element of space around a specific place. An orbit involves information about an electron's precise path or trajectory across the space that an electron itself cannot possess. An orbital is not a physical reality like the wave function but a mathematical feature which provides the density distribution of the electron physically observable when squared.