Skip to main content

Silicon has three naturally occurring isotopes (Si-28,Si-29,Si-30). The mass and natural abundance of Si-28 are 27.9769 amu and 92.2% respectively....

First, let me list down the given information:


Si-28, 27.9769 amu, 92.20%


Si-29, 28.9765 amu, 4.67% 


Si has an atomic weight of 28.0855 amu (while this is not given, the information should be readily available in the periodic table. this is a crucial bit of information as you will see in the solution below.)


The problem mentions that there are three isotopes. Hence, Si-28, Si-29, and Si-30 are all the isotopes of silicon and should make up 100% of the silicon in the world. This allows us to calculate the abundance of Si-30 - the sum of abundance of all isotopes should be 100%:


Abundance of Si-30 = 100 - 92.2 - 4.67 = 3.13


Hence, 3.13% of all silicon reserves is silicon-30.


The atomic weight of an element (listed in a reference such as the periodic table) is they weighted average of the masses of its isotopes. Hence, 28.0855 amu, the atomic weight of silicon, is a weighted average of the individual masses of its isotopes - that is, the mass multiplied by its abundance.


Hence (let m be atomic mass and a be abundance):


mSi = mSi28*aSi28 + mSi29*aSi29 + mSi30*aSi30


28.0855 = 27.9769*0.922 + 28.9756*0.0467 + 0.0313X.


Here, X is the atomic mass of silicon-30, which we do not know yet.


Doing the calculation, you end up with;


0.0313X = 0.93763768


X = 29.9565


This means that Silicon-30 has an atomic mass of 29.9565 amu (which makes sense cause this rounds up to 30, the basis of the names of the isotopes).


---


Note: you can check if this is right by calculating the atomic mass of silicon based on the abundance and masses of its isotopes.

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