Abstract:
A computerized method and system for demonstrating and teaching electron configurations in atomic structure are disclosed. One method includes presenting to a user one or more user interfaces stored in memory of the computing system, the one or more user interfaces includes a plurality of electron configuration diagrams. The method also includes receiving user input into an orbital box diagram displayed in the one or more user interfaces, the user input defining a possible electron configuration. The method further includes in response to the user input, updating the one or more user interfaces to illustrate the electron configuration received from the user, and if instructed by the user, generates a report regarding the compliance of the user-entered electron configuration with one or more electron configuration rules.

Description:
BACKGROUND 
       [0001]    Atomic structure is typically taught as a part of a high school or college chemistry curriculum. Lessons included in that curriculum often cover information about electron configurations, including atomic orbitals, valence electrons, and various rules used to determine the positions and energy levels of those electrons. In existing curricula, these lessons are provided in textbooks, which include a number of exercises that require students to draw orbital box diagrams and atomic orbitals, and to determine valid electron configurations that will not violate a number of rules (e.g., the Pauli Exclusion Principle, Hund&#39;s Rule, and the Aufbau principle). 
         [0002]    It can be difficult for students to visualize and make connections between a number of aspects of electron configurations, such as how atomic orbitals fit together in three-dimensional space, the relationship between an element&#39;s electron configuration and its position in the periodic table, and the relationships between electron configuration, atomic orbitals, and valence electrons (e.g., as illustrated in electron dot diagrams). Students must manually draw each of these diagrams and may have a difficult time both visualizing the correct configuration and determining when their diagrammed configuration is correct or incorrect. 
       SUMMARY 
       [0003]    In accordance with the following disclosure, the above and other problems are solved by: 
         [0004]    In a first aspect, a computerized method for visually demonstrating and teaching electron configuration in an atomic structure is disclosed. The method includes presenting to a user one or more user interfaces stored in memory of the computing system, the one or more user interfaces including a plurality of representations of an atom&#39;s electron configuration (electron configuration diagrams). The method also includes receiving user input into an orbital box diagram displayed in the one or more user interfaces, the user input defining a possible electron configuration. The method further includes in response to the user input, updating the one or more user interfaces to illustrate the electron configuration received from the user. 
         [0005]    In a second aspect, an electron configuration teaching system includes a display, a memory, and a programmable circuit. The memory is configured to store a plurality of user interfaces capable of presentation on the display, the plurality of user interfaces that implement a plurality of electron configuration diagrams. The programmable circuit is operatively connected to the display and the memory and is configured to execute program instructions to present on the display one or more of the user interfaces. The programmable circuit is further configured to execute program instructions to receive user input into an orbital box diagram displayed in the one or more user interfaces, the user input defining a possible electron configuration, and to update the one or more user interfaces to illustrate the electron configuration received from the user. 
         [0006]    In a third aspect, a computerized method of demonstrating electron configuration in an atomic structure includes presenting to a user one or more user interfaces stored in memory of the computing system, the one or more user interfaces including a plurality of electron configuration diagrams including an atomic orbital simulation, an electron dot diagram, a periodic table, an alphanumeric representation, and an orbital box diagram. The computerized method also includes receiving user input into the orbital box diagram defining a possible electron configuration, and, in response to the user input, updating the one or more user interfaces to illustrate the electron configuration received from the user. The computerized method further includes, upon user request, generating a report regarding compliance of the user-entered electron configuration with one or more electron configuration rules. 
     
    
     
       DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  is a flowchart of methods and systems for computerized modeling of electron configurations, according to certain embodiments of the present disclosure; 
           [0008]      FIG. 2  is a block diagram illustrating example physical components of an electronic computing device useable to implement the various methods and systems described herein; 
           [0009]      FIG. 3A  illustrates a user interface capable of displaying an atomic orbital simulation that represents the spatial distribution of an electron in an atom, according to possible embodiments of the present disclosure; 
           [0010]      FIG. 3B  illustrates a user interface for user-manipulation of a model of electron configurations in an atom, according to possible embodiments of the present disclosure; 
           [0011]      FIG. 4A  illustrates an example implementation of the user interface of  FIG. 3A  displaying the atomic orbital simulation of a hydrogen atom; 
           [0012]      FIG. 4B  illustrates an example implementation of the user interface of  FIG. 3B  to cause the atomic orbital simulation shown in  FIG. 4A  relating to the hydrogen atom; 
           [0013]      FIG. 4C  illustrates an example user interface displaying electron configuration validity status for the electron configuration of  FIGS. 4A-4B , according to a possible embodiment of the present disclosure; 
           [0014]      FIG. 5A  illustrates an example implementation of the user interface of  FIG. 3A  displaying the atomic orbital simulation of an aluminum atom; 
           [0015]      FIG. 5B  illustrates an example implementation of the user interface of  FIG. 3B  to cause the atomic orbital simulation shown in  FIG. 5A  relating to the aluminum atom; 
           [0016]      FIG. 5C  illustrates an example user interface displaying electron configuration validity status for the electron configuration of  FIGS. 5A-5B , according to a possible embodiment of the present disclosure; 
           [0017]      FIG. 6A  illustrates an example implementation of the user interface of  FIG. 3A  displaying the atomic orbital simulation of a helium atom; 
           [0018]      FIG. 6B  illustrates an example implementation of the user interface of  FIG. 3B  to cause the atomic orbital simulation shown in  FIG. 6A  relating to the helium atom; 
           [0019]      FIG. 6C  illustrates an example user interface displaying electron configuration validity status for the electron configuration of  FIGS. 6A-6B , according to a possible embodiment of the present disclosure; 
           [0020]      FIG. 7A  illustrates an example implementation of the user interface of  FIG. 3A  displaying the atomic orbital simulation of a beryllium atom; 
           [0021]      FIG. 7B  illustrates an example implementation of the user interface of  FIG. 3B , to cause the atomic orbital simulation shown in  FIG. 6A  relating to the beryllium atom; 
           [0022]      FIG. 7C  illustrates an example user interface displaying electron configuration validity status for the electron configuration of  FIGS. 7A-7B , according to a possible embodiment of the present disclosure; 
           [0023]      FIG. 7D  illustrates the user interface of  FIG. 7A  after a first user manipulation to label and to separate atomic orbitals; and 
           [0024]      FIG. 7E  illustrates the user interface of  FIG. 7D  after a further user manipulation to separate atomic orbitals. 
           [0025]      FIG. 8  illustrates an example interface for an online lesson. 
       
    
    
     DETAILED DESCRIPTION 
       [0026]    Various embodiments of the present disclosure will be described in detail with reference to the drawings, wherein like reference numerals represent like parts and assemblies throughout the several views. Reference to various embodiments does not limit the scope of the disclosure. Additionally, any examples set forth in this specification are not intended to be limiting and merely set forth some of the many possible embodiments related to the disclosure herein. 
         [0027]    The logical operations of the various embodiments of the disclosure described herein are implemented as: (1) a sequence of computer implemented steps, operations, or procedures running on a programmable circuit within a computer, and/or (2) a sequence of computer implemented steps, operations, or procedures running on a programmable circuit within a directory system, database, or compiler. 
         [0028]    In general the present disclosure relates to methods and systems for demonstrating and teaching electron configuration in an atomic structure. In particular, the present disclosure relates to computerized, interactive electron configuration diagrams that illustrate the connections between various concepts of atomic structure and simulate atomic orbitals, based on input electron configurations, and optionally checks input electron configurations for violations of electron configuration rules. This demonstration and teaching system can be incorporated, for example, into any of a number of types of computerized lessons or generalized curricula. 
         [0029]    Referring now to  FIG. 1 , a flowchart  100  of methods and systems for computerized modeling of electron configurations are shown, according to certain embodiments of the present disclosure. The methods and systems illustrated by flowchart  100  can be executed on a computer, such as the one described below in conjunction with  FIG. 2 , or can be hosted at a server computer, with the various user interfaces described herein communicated to a remote system. The displayed user interfaces are in either instance used by teachers or students or others having interest in the curriculum (collectively “users”). 
         [0030]    The flowchart  100  is instantiated at a start operation  102 , which corresponds to initializing software on a computing system, for example by selecting software or a lesson within such software (see  FIG. 8 ) that causes initialization of the electron configuration demonstration software. 
         [0031]    Operational flow proceeds to a display lesson module  104 , which displays a lesson associated with atomic structure and electron configuration. The lesson can include, for example, textual or graphical demonstrations of manipulation of electron configurations in orbital box diagrams and illustrations of various electron distributions among atomic orbitals, and rules related thereto. 
         [0032]    One example of such a lesson is shown in  FIG. 8 . A user interface  400  includes a unit module  402  that allows the users to select a unit for the lesson, and an experiment module that allows the users to select an experiment associated with the selected unit. A description module  406  provides a description related to the selected unit and/or experiment. 
         [0033]    In example embodiments described herein, the modeling of electron configurations is provided in conjunction with the online lesson. In other examples, the modeling can be provided in conjunction with a written lesson. In yet other examples, the modeling can be provided separate from any lesson or in conjunction with other curricula. Other configurations are possible. 
         [0034]    Referring again to  FIG. 1 , the display lesson module  104  includes generation of one or more user interfaces that are configured to be presented on display user interfaces, at least one of which includes an electron configuration diagram. The electron configuration diagram can take any of a number of forms. In certain embodiments, the electron configuration diagram includes a simulated atom including various atomic orbitals, e.g., s, p, d, and f atomic orbitals. Other electron configuration diagrams (e.g., electron dot diagrams, alphanumeric representations, schematic diagrams, a periodic table, or other types of diagrams) could be used as well. One example diagram and associated user interface for entering user electron configurations is shown in  FIGS. 3A-3B , described below. 
         [0035]    A user electron configuration module  106  receives user input regarding a possible electron configuration at the computing system that executes or communicates data related to the methods and systems described herein. The user electron configuration module  106  can, in certain embodiments, receive the electron configuration from a user by receiving selection of particular boxes in an orbital box diagram, allowing the user to select the particular orbital, pair, and spin for each individual electron. Example user electron configurations are shown in  FIGS. 4B ,  5 B,  6 B, and  7 B, below. 
         [0036]    A display module  108  presents one or more of the user interfaces displayed to a user to reflect the particular electron configuration selected by the user. In certain embodiments, the display module can update existing user interface features to reflect a particular received electron configuration. In other embodiments, the display module  108  creates new user interfaces, such as a periodic table and an electron dot diagram of the atom reflected by the electron configuration. Example user electron configuration displays and representations of electron configurations are shown in  FIGS. 4A ,  4 B,  5 A,  5 B,  6 A,  6 B,  7 A, and  7 B, below. 
         [0037]    A user manipulation module  110  allows user manipulation of one or more of the various user interfaces displaying the electron configuration. As compared to the user electron configuration module  106 , the user manipulation module  110  accepts manipulation of one or more of the graphical user interfaces, rather than modification of the current electron configuration. For example, the user manipulation module  110  can receive information relating to electron animation, separation of atomic orbitals, rotation of a simulated atom, movement or pivoting of the simulated atom, labeling of orbitals, or other view modification operations. Example graphical modifications are shown in  FIGS. 7A ,  7 B,  7 D, and  7 E, described below. 
         [0038]    An electron configuration check operation  112  receives user selection of an electron configuration check option in a user interface (e.g., as described below in conjunction with user interface  3 B). If the electron configuration check operation is selected, operational flow branches “yes” and proceeds to a configuration rules module  114 . 
         [0039]    The electron configuration rules module  114  determines, based on the electron configuration provided by the user into the receive user electron configuration module  106 , whether any electron configuration rules are violated. In certain embodiments described herein, three rules that are tested include the Pauli Exclusion Principle, Hund&#39;s Rule, and the Aufbau principle. 
         [0040]    The Aufbau Principle requires that all electrons occupy atomic orbitals of the lowest energy level available. For example, if the is orbital remains open, the next electron added to an atom will join that orbital. If the is orbital is full (contains two electrons), the next electron will then reside in the 2s orbital. If the 2s orbital is full (contains two electrons), the next added electron will reside in a 2p orbital, and so on. 
         [0041]    Hund&#39;s rule requires that, within each energy level, each orbital receives a single electron before each orbital receives its pair of electrons that can reside in that orbital. For example, in the three 2p orbitals available, each orbital will obtain a single electron before any one orbital obtains a second electron. In addition, the spins of each of these unpaired electrons must be the same. 
         [0042]    The Pauli Exclusion Principle requires that, within each orbital, one electron will have “up” spin, while the other electron has “down” spin. 
         [0043]    The configuration rules module displays to a user the results of comparison of each of the above principles to the user-entered electron configuration, and optionally suggests modifications to the electron configuration to form a valid configuration. 
         [0044]    From the electron configuration rules module  114 , operational flow proceeds to an end operation  116 , which corresponds to completed analysis of the currently input electron configuration at the configuration rules module  114 . Additionally, if the electron configuration check operation is not selected, operational flow branches “no” to the end operation  116 . 
         [0045]    The end operation  116  does not necessarily refer to completion of execution of software, but rather merely completed analysis of the current electron configuration. Once another electron configuration is entered into a user interface (i.e., into the user electron configuration module  106 ), other modules could update other user interfaces (e.g., the atomic orbital simulation, alphanumeric representation, electron dot diagram, periodic table, or other user interface components). 
         [0046]    The various modules of the flowchart  100  need not necessarily execute in the order described herein. For example, following analysis of a particular electron configuration at the configuration rules module  114 , a user could modify the electron configuration (e.g., user electron configuration module  106 ), thereby causing an update to the display (e.g. operation of display module  108 ). However, following each new electron configuration input into a user interface and received by the user electron configuration module  106 , the display module  108  will execute and update electron configuration diagrams. Other arrangements are possible as well. 
         [0047]      FIG. 2  is a block diagram illustrating example physical components of an electronic computing device  200 , which can be used to execute the various operations described above with respect to  FIG. 1 . A computing device, such as electronic computing device  200 , typically includes at least some form of computer-readable media. Computer readable media can be any available media that can be accessed by the electronic computing device  200 . By way of example, and not limitation, computer-readable media might comprise computer storage media and communication media. 
         [0048]    As illustrated in the example of  FIG. 2 , electronic computing device  200  comprises a memory unit  202 . Memory unit  202  is a computer-readable data storage medium capable of storing data and/or instructions. Memory unit  202  may be a variety of different types of computer-readable storage media including, but not limited to, dynamic random access memory (DRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), reduced latency DRAM, DDR2 SDRAM, DDR3 SDRAM, Rambus RAM, or other types of computer-readable storage media. 
         [0049]    In addition, electronic computing device  200  comprises a processing unit  204 . As mentioned above, a processing unit is a set of one or more physical electronic integrated circuits that are capable of executing instructions. In a first example, processing unit  204  may execute software instructions that cause electronic computing device  200  to provide specific functionality. In this first example, processing unit  204  may be implemented as one or more processing cores and/or as one or more separate microprocessors. For instance, in this first example, processing unit  204  may be implemented as one or more Intel Core  2  microprocessors. Processing unit  204  may be capable of executing instructions in an instruction set, such as the x86 instruction set, the POWER instruction set, a RISC instruction set, the SPARC instruction set, the IA-64 instruction set, the MIPS instruction set, or another instruction set. In a second example, processing unit  204  may be implemented as an ASIC that provides specific functionality. In a third example, processing unit  204  may provide specific functionality by using an ASIC and by executing software instructions. 
         [0050]    Electronic computing device  200  also comprises a video interface  206 . Video interface  206  enables electronic computing device  200  to output video information to a display device  208 . Display device  208  may be a variety of different types of display devices. For instance, display device  208  may be a cathode-ray tube display, an LCD display panel, a plasma screen display panel, a touch-sensitive display panel, a LED array, or another type of display device. 
         [0051]    In addition, electronic computing device  200  includes a non-volatile storage device  210 . Non-volatile storage device  210  is a computer-readable data storage medium that is capable of storing data and/or instructions. Non-volatile storage device  210  may be a variety of different types of non-volatile storage devices. For example, non-volatile storage device  210  may be one or more hard disk drives, magnetic tape drives, CD-ROM drives, DVD-ROM drives, Blu-Ray disc drives, or other types of non-volatile storage devices. 
         [0052]    Electronic computing device  200  also includes an external component interface  212  that enables electronic computing device  200  to communicate with external components. As illustrated in the example of  FIG. 2 , external component interface  212  enables electronic computing device  200  to communicate with an input device  214  and an external storage device  216 . In one implementation of electronic computing device  200 , external component interface  212  is a Universal Serial Bus (USB) interface. 
         [0053]    In other implementations of electronic computing device  200 , electronic computing device  200  may include another type of interface that enables electronic computing device  200  to communicate with input devices and/or output devices. For instance, electronic computing device  200  may include a PS/2 interface. Input device  214  may be a variety of different types of devices including, but not limited to, keyboards, mice, trackballs, interactive whiteboards, stylus input devices, touch pads, touch-sensitive display screens, or other types of input devices. External storage device  216  may be a variety of different types of computer-readable data storage media including magnetic tape, flash memory modules, magnetic disk drives, optical disc drives, and other computer-readable data storage media. 
         [0054]    In the context of the electronic computing device  200 , computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data. Computer storage media includes, but is not limited to, various memory technologies listed above regarding memory unit  202 , non-volatile storage device  210 , or external storage device  216 , as well as other RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and that can be accessed by the electronic computing device  200 . 
         [0055]    In addition, electronic computing device  200  includes a network interface card  218  that enables electronic computing device  200  to send data to and receive data from an electronic communication network. Network interface card  218  may be a variety of different types of network interface. For example, network interface card  218  may be an Ethernet interface, a token-ring network interface, a fiber optic network interface, a wireless network interface (e.g., WiFi, WiMax, etc.), or another type of network interface. 
         [0056]    Electronic computing device  200  also includes a communications medium  220 . Communications medium  220  facilitates communication among the various components of electronic computing device  200 . Communications medium  220  may comprise one or more different types of communications media including, but not limited to, a PCI bus, a PCI Express bus, an accelerated graphics port (AGP) bus, an Infiniband interconnect, a serial Advanced Technology Attachment (ATA) interconnect, a parallel ATA interconnect, a Fiber Channel interconnect, a USB bus, a Small Computer System Interface (SCSI) interface, or another type of communications medium. 
         [0057]    Communication media, such as communications medium  220 , typically embodies computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” refers to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media includes wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared, and other wireless media. Combinations of any of the above should also be included within the scope of computer-readable media. Computer-readable media may also be referred to as computer program product. 
         [0058]    Example electronic computing device  200  includes several computer-readable data storage media (i.e., memory unit  202 , non-volatile storage device  210 , and external storage device  216 ). Together, these computer-readable storage media may constitute a single data storage system. As discussed above, a data storage system is a set of one or more computer-readable data storage mediums. This data storage system may store instructions executable by processing unit  204 . Activities described in the above description may result from the execution of the instructions stored on this data storage system. Thus, when this description says that a particular logical module performs a particular activity, such a statement may be interpreted to mean that instructions of the logical module, when executed by processing unit  204 , cause electronic computing device  200  to perform the activity. In other words, when this description says that a particular logical module performs a particular activity, a reader may interpret such a statement to mean that the instructions configure electronic computing device  200  such that electronic computing device  200  performs the particular activity. 
         [0059]    One of ordinary skill in the art will recognize that additional components, peripheral devices, communications interconnections and similar additional functionality may also be included within the electronic computing device  200  without departing from the spirit and scope of the present disclosure. 
         [0060]    In the examples described herein, the electronic computing device  200  executes instructions stored in memory to implement the systems and methods described herein. For example, the electronic computing device  200  can include a program stored in memory. When the electronic computing device  200  executes the program, the electronic computing device  200  creates and/or performs the modules/operations shown in  FIG. 1  and renders the user interfaces shown in  FIGS. 3-7 . 
         [0061]    Now referring to  FIGS. 3A-3B , user interfaces are illustrated that can be used to display models of atomic orbitals corresponding to various electron configurations. 
         [0062]      FIG. 3A  illustrates a user interface  300  capable of displaying the three-dimensional electron distribution in an atom. The electron distribution is represented as a “cloud” of small, colored points that represent positions where the electron is most likely to be found. User interface  300  also optionally presents an animation consisting of small spheres moving randomly among these positions of high probability, representing movement of the electron in the atomic orbital.  FIG. 3B  illustrates a user interface  320  useable for user-manipulation of electron configurations in an atom (an atomic orbital). User interface  300  of  FIG. 3A  includes a general display area  302  for displaying atomic orbital simulations surrounding a simulated nucleus of an atom. Display modification buttons  304  allow manipulation of the simulations, for example to rotate, pivot, move, zoom or reset the view displayed in area  302 . A slider bar  306  allows a user to separate atomic orbitals, thereby isolating each of the orbitals included in the displayed electron configuration (e.g., as shown and described in greater detail in conjunction with  FIGS. 7D-7E ). Check box  308  allows a user to elect to label the various orbitals included in the electron configuration (e.g., as shown in  FIGS. 7A ,  7 D, and  7 E). 
         [0063]    User interface  320  includes an orbital box diagram  322 , into which a user can enter electron configurations. The orbital box diagram  322  displays the various possible electron shells, or energy levels, and the orbitals into which the electrons can be placed. In the embodiment shown, the 1s, 2s, 2p, 3s, 3p, 4s, 3d, and 4p energy levels and associated orbitals are shown (i.e., a single orbital for each s energy level, three orbitals for each p energy level, and five orbitals for each d energy level). Each orbital includes a pair of electron positions. A user can select any of the boxes included in the orbital box diagram  322 , e.g., by clicking on the box in the user interface. In other examples, more or fewer shell levels (n&gt;4 or n&lt;4) can be shown. 
         [0064]    In certain embodiments, different numbers of clicks within a single box will change the presence and spin of an electron associated with that box (and associated shell/energy level). For example, in certain embodiments, a first mouse click causes an “up” spin electron to be placed into the box, a second mouse click changes the “up” spin electron to a “down” spin electron. A third mouse click can remove the electron from the box altogether. A clear button  324  allows clearance of each of the boxes in the orbital box diagram  322 . 
         [0065]    Each time a box is selected in the orbital box diagram  322  to cause addition (or removal) of an electron relating to a particular orbital, the corresponding display area  302  is altered accordingly to reflect the simulated atom as formed by the user. This display of the movement of electrons in the atomic orbital (animation) is based upon a mathematical formula representing the probability of the presence of an electron in any given position within an orbital at a particular time. A stop animation button  326  allows a user to pause the animation and analyze the “cloud” of points that represents the spatial extent of the orbitals occupied by the particular electron configuration. 
         [0066]    A check configuration button  328  allows a user to initiate a computer-based check of the validity of the particular electron configuration entered into the orbital box diagram  322  against electron configuration rules (e.g., the Pauli Exclusion Principle, Hund&#39;s Rule, and the Aufbau principle). Therefore, selection of the check configuration button  328  corresponds to selection of the “yes” option of the electron configuration check operation  112 , thereby leading to the configuration rules module  114 , which can generate a user interface displaying those test results. 
         [0067]    Additional details regarding the current electron configuration can be included in the user interface  320  as well. For example, an atomic symbol  330  (shown in  FIGS. 4B ,  5 B,  6 B, and  7 B) denotes the atom having the number of electrons currently selected by the user. Additionally, an electron count  332  includes the number of electrons currently included in the configuration, and an electron configuration listing  334  provides the alphanumeric representation of the electron configuration corresponding to that selected in the orbital box diagram  322 . 
         [0068]    Operation of the user interfaces of  FIGS. 3A-3B  are illustrated further in the examples of  FIGS. 4-7 .  FIGS. 4A-4B  show user interfaces  300 ,  320  upon entry of an electron configuration including a single electron in the 1s orbital. Upon entry of the electron in that orbital, a number of additional changes to user interfaces  300 ,  320  occur. For example, in display area  302  ( FIG. 4A ), a first atomic orbital  402  is displayed, indicating the presence of an electron in the is orbital. Additionally, in user interface  320  ( FIG. 4B ), the atomic symbol  330  for hydrogen appears (noted as “H”) and a total number of electrons is displayed. Additionally, the alphanumeric representation of the electron configuration  334  is displayed along a bottom edge of the user interface  320  (listed as “1s 1 ”). 
         [0069]    In addition, within the first atomic orbital  402 , a depiction of the electron  403  within the first orbital  402  is provided. In example embodiments, the depiction of the electron  403  within the first orbital  402  is animated to approximate a cloud of random, high-probability positions of the electron  403  within the first orbital  402 . 
         [0070]    For example, a wave function computation can be used to compute the value of the wave function of the one-electron Schrödinger equation for one atom of a selected element. These values are computed over a three-dimensional region of space surrounding the nucleus of the atom. The square of the wave function value at a given point in space is equal to the probability of finding the electron at that point. Because these calculations can be computationally time-consuming, the wave function values may be “pre-computed” and stored in computer memory or on magnetic (hard disk) storage, and read into program memory as needed. The resulting computations are used to place the electron  403  in likely positions within the first atomic orbital  402  at a given point in time. 
         [0071]    Further, in one example, the first atomic orbital  402  is rendered based on logic that reads the values of the electron wave function probabilities from memory and draws a representation of that computed region of three-dimensional space where the electron is likely to be found, within a selected probability. Examples of three-dimensional representations of the atomic orbitals include “clouds” of semi-transparent, colored points, as shown in  FIG. 4A . Other three-dimensional structures, such as isosurfaces that represent solids that contain all of the points of a selected probability, can also be used. 
         [0072]    When electrons are added to additional orbitals, the electron placement and orbital clouds are calculated and updated in a similar manner. See, for example,  FIG. 5A , which shows multiple orbitals  402 ,  404 ,  406 ,  408 , and  410 . 
         [0073]      FIG. 4C  illustrates an example user interface  350  displaying electron configuration validity status for the electron configuration of  FIGS. 4A-4B . User interface  350  therefore corresponds to the display of results generated by the configuration rules module  114  of  FIG. 1 . As shown, user interface  350  displays results of the comparison to electron configuration rules. In the example shown, because a single electron placed in the is orbital is a valid electron configuration for a hydrogen atom, all tests are indicated as passed. 
         [0074]      FIGS. 5A-5C  illustrate a further example of use of the user interfaces  300 ,  320 ,  350 , in conjunction with a valid aluminum atom. In this case, orbitals  402 ,  404 ,  406 ,  408 , and  410  are displayed in display area  302  of  FIG. 5A , corresponding to the 1s, 2s, 2p, 3s, and 3p orbitals. The atomic symbol  330  “Al” is shown in user interface  320 , and the alphanumeric representation of the electron configuration  334  (1s 2 2s 2 2p 6 3s 2 3p 1 ) is provided, along with the electron count  332 . 
         [0075]      FIG. 5C  illustrates user interface  350  displaying electron configuration validity status for the electron configuration of  FIGS. 5A-5B  showing that the electron configuration in orbital box diagram  322  shown in  FIG. 5B  is a valid configuration for an aluminum atom. Therefore, a user entering this configuration would be deemed to have entered a correct electron configuration, when using a lesson incorporating the methods and systems of the present disclosure. 
         [0076]      FIGS. 6A-6C  illustrate an example “invalid” electron configuration that violates one or more of the rules evaluated by the configuration rules module  114  of  FIG. 1 . In the embodiment shown, two electrons are placed in the orbital box diagram in the is orbital  402 , but both have “up” spin. The view in display area  302  of this electron configuration appears similar to that shown in  FIG. 4A , and the alphanumeric representation of the electron configuration  334  is shown as 1s 2  (the correct configuration). However, based on the two “up” spinning electrons, the configuration is deemed invalid under the Pauli Exclusion Principle, as shown in user interface  350  as shown in  FIG. 6C . Therefore, a student or teacher entering this configuration would be required to correct the configuration prior to being deemed correct in the lesson in which the methods and systems of the present disclosure are incorporated. 
         [0077]      FIGS. 7A-7E  illustrate an example invalid electron configuration of a beryllium atom, and also illustrate certain additional graphical features of the present application that were mentioned briefly in conjunction with  FIG. 1 , above.  FIG. 7A  shows user interface  300  displaying an electron configuration of a beryllium atom;  FIG. 7B  shows user interface  320  with the corresponding entered electron configuration in the orbital box diagram  322 . As shown, a user has entered one “up” electron in the 1s orbital, one “up” electron in the 2s orbital, and two “up” electrons in one of the 2p orbitals, therefore representing an overall electron configuration  334  of 1s 1 2s 1 2p 2 . These four electrons correspond to the total number of electrons in a beryllium atom, but represent an invalid electron configuration. As illustrated in  FIG. 7C , this electron configuration violates all of the Pauli Exclusion Principle, Hund&#39;s Rule, and the Aufbau principle. 
         [0078]    In  FIGS. 7A-7B , certain additional features are shown. In user interface  300 , check box  308  is selected, and labels  702 ,  704 ,  706  appeared next to the 1s, 2s, and 2p orbitals  402 ,  404 ,  406 , respectively. 
         [0079]    In user interface  320 , an electron dot diagram  722  is displayed around the atomic symbol  330  for the atom having the user-entered electron configuration. In the example shown, two dots are displayed on a single side of the “Be” symbol, indicating that two valence electrons exist in a single orbital (in this case, all of the electron configurations rules have been violated, and the two electrons shown at the 2p energy level should first fill the 1s and 2s energy levels, making 2s the valence energy level). 
         [0080]    Additionally, a periodic table  724  is displayed. In one example, the periodic table  724  is configured to highlight the currently-configured element within the periodic table. In another example, only a specific sub-set of elements are displayed, such as the noble gases (i.e., He, Ne, Ar, Kr). In one example, the user can click on the noble gases within the periodic table  724 , and the orbital box diagram  322  is filled with the electrons corresponding to the selected noble gas and the alphanumeric representation of the electron configuration employs a noble gas “shorthand” notation. In other examples, the user can click on any element in the periodic table  724 , and thereupon the orbital box diagram  322  is filled out for that selected element. 
         [0081]    In another example, the various elements in the periodic table  724  are highlighted as the user adds electrons to the orbital box diagram  322 . For example, if the user adds two electrons to the is orbital, the element helium (He) is highlighted to illustrate to the user that this electron configuration represents He. Other configurations are possible. 
         [0082]      FIGS. 7D-7E  illustrate stages of operation of slider bar  306  in the user interface  300 , separating the 1s, 2s, and 2p orbitals of the beryllium atom as entered (incorrectly) into the orbital box diagram  322  of  FIG. 7B .  FIG. 7E  illustrates orbitals  402 ,  404 ,  406  fully separated, with the slider bar  306  positioned to the far right side of the user interface  300 .  FIG. 7D  illustrates orbitals  402 ,  404 ,  406  partially separated, as the slider bar  306  is positioned at a midpoint between a default overlapping arrangement (e.g., as shown in  FIG. 7A ), and a fully separated arrangement (shown in  FIG. 7E ). 
         [0083]    Other configurations for the systems and methods described herein are possible. For example, in one alternative, the orbital box diagram can be replaced with another model used to represent electron configurations, such as a line notation that uses horizontal line segments over which representations of electrons are drawn or circle notation in which representations of electrons are drawn. 
         [0084]    In addition, the examples described herein use cloud diagrams to visually represent the atomic orbitals. However, other configurations, such as isosurfaces, can also be used to represent one or more of the orbitals. 
         [0085]    In use, the computerized teaching systems and methods of the present disclosure improve the efficiency and ease with which students or other users are taught about and can explore electron configurations in atoms and with which teachers can demonstrate and lecture about electron configuration in atoms. These systems and methods provide interactive feedback to the student regarding valid and invalid electron configurations, improve visualization of the atomic orbital arrangements of various atoms, and improve students&#39; synthesis of the relationships between atomic structure, valence electrons (important in chemical bonding) as depicted in electron dot diagrams, and the periodic table&#39;s representation of the relationships between the elements. 
         [0086]    The various embodiments described above are provided by way of illustration only and should not be construed to be limiting. Various modifications and changes may be made to the embodiments described above without departing from the true spirit and scope of the disclosure.