Hund's rule states that if two or more orbitals with the same energy are available, one electron goes in each until all are half full.
The electrons in the half-filled orbitals all have the same value of their spin quantum number. What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Quantum Numbers: Angular Momentum Quantum Number concept. If you forgot your password, you can reset it. Join thousands of students and gain free access to 46 hours of Chemistry videos that follow the topics your textbook covers. Analytical Chemistry Video Lessons. Cell Biology Video Lessons. Genetics Video Lessons. Biochemistry Video Lessons. GOB Video Lessons. Microbiology Video Lessons.
Calculus Video Lessons. Statistics Video Lessons. Microeconomics Video Lessons. Macroeconomics Video Lessons. Accounting Video Lessons. Join Clutch Prep Get a better grade with hundreds of hours of expert tutoring videos for your textbook Continue Continue OR Password must contain at least one uppercase letter, a number and a specific symbol.
Experimental evidence suggests that an orbital can hold no more than two electrons. To distinguish between the two electrons in an orbital, we need a fourth quantum number.
This is called the spin quantum number s because electrons behave as if they were spinning in either a clockwise or counterclockwise fashion.
Thus, it takes three quantum numbers to define an orbital but four quantum numbers to identify one of the electrons that can occupy the orbital. The allowed combinations of n , l , and m quantum numbers for the first four shells are given in the table below. For each of these orbitals, there are two allowed values of the spin quantum number, s. Summary of Allowed Combinations of Quantum Numbers. Because of the force of attraction between objects of opposite charge, the most important factor influencing the energy of an orbital is its size and therefore the value of the principal quantum number, n.
For an atom that contains only one electron, there is no difference between the energies of the different subshells within a shell. The 3 s , 3 p , and 3 d orbitals, for example, have the same energy in a hydrogen atom. The Bohr model, which specified the energies of orbits in terms of nothing more than the distance between the electron and the nucleus, therefore works for this atom.
The hydrogen atom is unusual, however. As soon as an atom contains more than one electron, the different subshells no longer have the same energy. Within a given shell, the s orbitals always have the lowest energy. The energy of the subshells gradually becomes larger as the value of the angular quantum number becomes larger.
As a result, two factors control the energy of an orbital for most atoms: the size of the orbital and its shape, as shown in the figure below. A very simple device can be constructed to estimate the relative energies of atomic orbitals. The allowed combinations of the n and l quantum numbers are organized in a table, as shown in the figure below and arrows are drawn at 45 degree angles pointing toward the bottom left corner of the table.
The order of increasing energy of the orbitals is then read off by following these arrows, starting at the top of the first line and then proceeding on to the second, third, fourth lines, and so on.
This diagram predicts the following order of increasing energy for atomic orbitals. The electron configuration of an atom describes the orbitals occupied by electrons on the atom. The basis of this prediction is a rule known as the aufbau principle , which assumes that electrons are added to an atom, one at a time, starting with the lowest energy orbital, until all of the electrons have been placed in an appropriate orbital.
This is indicated by writing a superscript "1" after the symbol for the orbital. The next element has two electrons and the second electron fills the 1 s orbital because there are only two possible values for the spin quantum number used to distinguish between the electrons in an orbital. After the 1 s and 2 s orbitals have been filled, the next lowest energy orbitals are the three 2 p orbitals.
The fifth electron therefore goes into one of these orbitals. However, there are three orbitals in the 2 p subshell. Does the second electron go into the same orbital as the first, or does it go into one of the other orbitals in this subshell? To answer this, we need to understand the concept of degenerate orbitals.
By definition, orbitals are degenerate when they have the same energy. The energy of an orbital depends on both its size and its shape because the electron spends more of its time further from the nucleus of the atom as the orbital becomes larger or the shape becomes more complex.
In an isolated atom, however, the energy of an orbital doesn't depend on the direction in which it points in space. Orbitals that differ only in their orientation in space, such as the 2 p x , 2 p y , and 2 p z orbitals, are therefore degenerate.
Electrons fill degenerate orbitals according to rules first stated by Friedrich Hund. Hund's rules can be summarized as follows. One electron is added to each of the degenerate orbitals in a subshell before two electrons are added to any orbital in the subshell. Electrons are added to a subshell with the same value of the spin quantum number until each orbital in the subshell has at least one electron.
When the time comes to place two electrons into the 2 p subshell we put one electron into each of two of these orbitals. The choice between the 2 p x , 2 p y , and 2 p z orbitals is purely arbitrary. Because each orbital in this subshell now contains one electron, the next electron added to the subshell must have the opposite spin quantum number, thereby filling one of the 2 p orbitals. There is something unusually stable about atoms, such as He and Ne, that have electron configurations with filled shells of orbitals.
By convention, we therefore write abbreviated electron configurations in terms of the number of electrons beyond the previous element with a filled-shell electron configuration. Electron configurations of the next two elements in the periodic table, for example, could be written as follows. Click here to check your answer to Practice Problem 8 The aufbau process can be used to predict the electron configuration for an element.
The actual configuration used by the element has to be determined experimentally. The experimentally determined electron configurations for the elements in the first four rows of the periodic table are given in the table in the following section. Exceptions to Predicted Electron Configurations. There are several patterns in the electron configurations listed in the table in the previous section. One of the most striking is the remarkable level of agreement between these configurations and the configurations we would predict.
There are only two exceptions among the first 40 elements: chromium and copper. Strict adherence to the rules of the aufbau process would predict the following electron configurations for chromium and copper. The experimentally determined electron configurations for these elements are slightly different.
0コメント