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Chapter 7: Problem 71

What is the physical significance of the value of \(\psi^{2}\) at a particular point in an atomic orbital?

Short Answer

Expert verified
The physical significance of the value of \(\psi^2\) at a particular point in an atomic orbital is that it represents the probability density of finding an electron at that location. A higher value of \(\psi^2\) indicates a greater likelihood of the electron being present in that specific region, while a lower value denotes a lower probability. This helps in visualizing electron distribution in atomic orbitals and understanding their shapes and properties.

Step by step solution

01

Understanding the wave function

The wave function, denoted by \(\psi\), is a mathematical representation of the electron's quantum state within an atom. It provides information about the probability of the electron's position, momentum, and other properties.
02

Squaring the wave function

By squaring the wave function (\(\psi^2\)), we obtain the probability density. Probability density is used to determine the likelihood of finding a particle in a given region of space. In other words, the higher the value of \(\psi^2\) at a point, the more probable it is to find an electron in that region.
03

Probability density in atomic orbitals

In atomic orbitals, \(\psi^2\) represents the probability density of finding an electron in a specific location around the nucleus. It is essential to emphasize that \(\psi^2\) is not an exact position but rather an indication of the electron's probability distribution across space.
04

Physical significance of \(\psi^2\) in an atomic orbital

The physical significance of the value of \(\psi^2\) in an atomic orbital relates to the likelihood of finding an electron at that particular point. A higher value of \(\psi^2\) signifies a higher probability that the electron will be found in that location, while a lower value indicates a lower probability. This information allows us to visualize the electron distribution in atomic orbitals and understand their shapes and properties.

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Most popular questions from this chapter

A photon of ultraviolet (UV) light possesses enough energy to mutate a strand of human DNA. What is the energy of a single UV photon and a mole of UV photons having a wavelength of \(25 \mathrm{~nm} ?\)

For each of the following pairs of elements \((\mathrm{C}\) and \(\mathrm{N}) \quad(\mathrm{Ar}\) and \(\mathrm{Br})\) pick the atom with a. more favorable (exothermic) electron affinity. b. higher ionization energy. c. larger size.

Using only the periodic table inside the front cover of the text, write the expected ground-state electron configurations for a. the third element in Group \(5 \mathrm{~A}\). b. element number 116 . c. an element with three unpaired \(5 d\) electrons. d. the halogen with electrons in the \(6 p\) atomic orbitals.

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms? a. The principal quantum number completely determines the energy of a given electron. b. The angular momentum quantum number, \(\ell\), determines the shapes of the atomic orbitals. c. The magnetic quantum number, \(m_{\ell}\), determines the direction that the atomic orbitals point in space.

Cesium was discovered in natural mineral waters in 1860 by R. W. Bunsen and G. R. Kirchhoff using the spectroscope they invented in \(1859 .\) The name came from the Latin caesius ("sky blue") because of the prominent blue line observed for this element at \(455.5 \mathrm{~nm} .\) Calculate the frequency and energy of a photon of this light.
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