Skip to main content

What is the set of four quantum numbers for last electron of aluminum and beryllium?

Quantum numbers are theoretical expressions representing certain quantum mechanical properties of sub-atomic particles, atoms, or molecules. 


In atoms and electrons, quantum numbers are used to describe the orbitals in atoms, mathematical representations of the likelihood of finding electrons in a given space. There are four quantum numbers:


  • Principal quantum number (n) - is generally related to the size of the orbital, or the distance of the electron from the nucleus. This also correspond to the energy level. Allowed values from n are 1, 2, 3, ... and where an increasing number of n refer to an increasing size or distance.

  • Angular quantum number (l) - describes the shape of the orbital. Orbitals can be spherical (s), can contain two lobes with a node in the middle (p), or four equally-spaced lobes with a node in the center (d), among others. These shapes correspond to a number: s is 0, p is 1, d is 2, f is 3, g is 4, ... Allowed numbers for this quantum number are 0 up to n-1. Hence, if the principal quantum number is 1, the only allowed shape is an s-orbital.

  • Magnetic quantum number (ml) - describes the orientation of an orbital in space, and may take on values from -l to +l. The d orbital, with l=2, can therefore have 5 different orientations each represented by a magnetic quantum number of -2, -1, 0, 1, 2.

  • Spin quantum number (ms) - describes the spin state of an electron in this case, and can only take on values of +1/2 and -1/2.


These quantum numbers may be derived from the electron configuration corresponding to an electron - for instance, the last electron. The electron configuration of aluminum is:


[Ne] 3s2 3p1,


Hence, the last electron is in 3p1. The n quantum number then is 3, as this is the 3rd energy level. The l quantum number is 1, which corresponds to the p orbital. The p orbital has three orientations - -1, 0, +1, and there is only one electron - the -1 orientation is conventionally filled out first (though these have equal likelihood to be filled out and these numbers are simplified representations). Moreover, if it is the first electron in a sub-shell, +1/2 is typically assigned. Hence, the last electron of aluminum will have the following QN:


n = 3, l = 1, ml = -1, ms = +1/2


Meanwhile, the last electron of beryllium has the following electron configuration:


[He] 2s2,


Hence, the n quantum number is 2, and the l quantum number is 0. There is only one possible ml for the s orbital and that is 0 - there are no other possible unique orientations for a sphere in 3D space. There are two electrons in this orbital - the first gets +1/2 spin, and the second -1/2. Hence, the last electron will have the following QN:


n = 2, l = 0, ml = 0, ms = -1/2

Comments

Post a Comment

Popular posts from this blog

etymology - Origin of the greeting "Sweet dreams".

Does anybody know the etymology of the phrase "sweet dreams"? I tried googling but did not find anything satisfying. Is this a relatively new phrase of the modern world or has this been in use for some time? I think it's the latter one. Answer The OED has the interjection as "a farewell to someone going to bed" from the 20th century: 1908 Sears Roebuck Catal. 198/1 Tenor Solos..Good Bye, Sweet Dreams, Good Bye. But it goes back until at least the 19th and possibly 18th centuries. John Wolcot, writing under the pseudonym of Peter Pindar, used it in his poem "Orson and Ellen; A Legendary Tale" published in 1801: Also from 1801 in The infernal Quixote (Page 287) by Charles Lucas: In the March 1776 of The Universal Magazine was published "The Serenade. A Pastoral Tale. From the German of Gesner" , where the shepherd Daphnis watches over his beloved as she sleeps and sings: The same tale appears in 1776's as Idyl XI, " Daphnis ...
Post a Comment
Read more

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

What are the similarities between the relationships of the characters in The Outsiders and Romeo and Juliet?

At first glance, it might appear as if the characters in  The Outsiders  by S. E. Hinton and  Romeo and Juliet  by William Shakespeare do not have much in common; however, when one isolates the core of the conflicts, it becomes clear that the relationships in both stories are rooted in rivalry and secrecy.  In both  The Outsiders  and  Romeo and Juliet , an overarching theme is rivalry. While   socioeconomic status separates the greasers from the Socs in The Outsiders , last names separates the Montagues from the Capulets, who appear to be relatively equal in terms of socioeconomic status. Due to these rivalries, there are instances of deadly interactions in both stories. In  The Outsiders , Johnny kills Bob (whether his actions were justified or not is debatable). In  Romeo and Juliet , Romeo kills Tybalt and Paris, and Tybalt kills Mercutio. These deaths have profound effects on the main characters. In Ponyboy's case, the Johnny's death and other events in the novel inspire h...
Post a Comment
Read more