Algebra 2 text-book prescribed for high school students in California is very large and heavy. Kids are likely to find it challenging lifting it with one hand. If they are small then they probably need to use both hands.
Isn’t the book heavy and unwieldy ? Would the book cause internal injury to abdomen if the kid drops it by mistake on their stomach while reading it lying on bed like they are used to reading story books?
Why can’t math text-book be simpler both in form factor and weight like the ones used in India? Even if they want to keep the content as they have now, could they have split the book into two volumes – one for first half of the school year and one for the 2nd half?
Should California import Math books from India? The text books used in India are simple, are paperback editions, short and sweet, and more importantly keep the content to the point. No silly skiing example to explain linear or quadratic equations.
How could California, the state that produced iPhone using the Zen principles simplicity, not produce a better text-book product? Did the product team that was in charge of the book knew how to design and present the product? How could they use so many colors, particularly strong primary colors for boxes, tables and for others? The colors strike reader’s eye so strong that it takes effort to find the main text amidst the glitter and glare.
Above all , why would a state like CA use so much chemical required to print in color given it is the most progressive one with respect to safeguarding the environment? Could it have supplied students with Kindles loaded with text books instead of printed books? Why print heavy books and in particular ones like the Algebra 2 text-book that is close to 1000 pages long?
This post is a reading aid for Chapter 5 : Periodic Table from ‘Modern Chemistry’ by HRW for 10th grade students of California. Could be useful for parents and teachers as well.
This chapter is relatively easy compared to the previous one. HRW team has done a good job of organizing the material around three logical and easy to read sections :
- Section 1: History behind Periodic Table
- Section 2: Periods, Groups and Blocks of Periodic Table
- Section 3: Atomic property trends across a row/ period and across column/group
Section 3 is bit dry and could be difficult for students. This reading aid will try to distill that section to the extent possible.
Knowing electron configurations from Chapter 4 is very important to sail through section 2 and 3 of this chapter. So keep going back to Chapter 4 as you read chapter 5. Alternatively, review Teaching Atomic Model for Facebook generation if you have difficulty reading the original Chapter 4 from HRW.
First, let us look at some facts related to periodic table that may come handy for your school test. Do notice text in bold.
Section 1: Facts and History of Periodic Table
- In 1860, Cannizzaro, an Italian scientist, proposed method for determining atomic mass of element
- In 1869, Mendeleeve, a Russian teacher and scientist, published world’s first periodic table in a school text book. There were about 60 known elements in the table with some spots left for elements Mendeleev predicted would be discovered!
- In 1911, Mosley, an English scientist, was able to correlate periodicity (elements with similar characteristics re-appearing in periodic table) with atomic number which led to formal definition of periodic law:
physical and chemical properties of elements are periodic functions of their atomic number
- Scandium (Sc), Gallium(Ga), Germanium (Ge) are three elements that were unnamed in Mendeleev’s first periodic table and discovered later
Before we dive further into contents of the chapter, please take time to reflect on these two questions
1. How many metals, liquids and gas elements do you know? Visualize your kitchen, garage, bath room, your family jewelry, or what you eat, drink , and breath daily.
think for at least 5 minutes and note down names of elements that flash as you think
2. What you understand by periodicity? don’t worry about periodic table. Just think about the word ‘periodic’ and see what crosses your mind.
think for 2 minutes
If you come up with about 20 elements then you are not too far off from Mendeleev! He knew about 60 elements in 1860.
What is Periodicity ?
To understand periodicity, let us look at some real world examples:
- A BART train leaves from Fremont every 30 mins. So periodicity is 30 minutes
- Each day, at 4am, there is a goods train that passes through Fremont. So periodicity for the goods train is 24 hours.
- Sun rises every morning. Periodicity for Sun rise is 24 hours
- Ocean wave has ups and downs as it travels. Its periodicity is determined by the length of the wave as measured from zero (flat) to high (peak) and back to zero. The length could be specified in meters/feet. (BTW, see Note 1 below for some advanced remarks on waves).
As you can see, all of the above have different periodicity (recurrence). The repeat interval is specified using different units such as hours and meters. Of course, the same train comes back, the same sun rises, and the same ocean wave repeats its ups and downs.
While organizing elements based on their physical/chemical properties, Mendeleev observed elements with similar properties re-appearing in his table. We can call related element as siblings. In periodic table there are several elements with as many as 7 siblings.
Though Mendeleev and others recognized elements with similar properties repeating at some periodic intervals in the table it was not clear to them as to:
- Why elements of same properties are re-appearing periodically
- How to correlate periodicity with properties of elements
- Why there are at most 7 siblings ? We may never know. But there is a myth around the mystery number 7. See note 2 if you have time.
- Infants in their 1st week need nursing every 3 hours. Periodicity =3 hours
- Infants in their 2nd week need nursing every 4 hours. Periodicity = 4 hours
- Infants in their 2nd month perhaps need nursing every 6 hours. Periodicity =6 hours
- Infants in their 3rd month need nursing every 8 hours. Periodicity=8 hours
As you can see different age group infants have different periodicity with respect to nursing. The time gap for nursing increases for older infants. Likewise, sibling elements (i.e ones with similar properties) repeat after some intervals. As the elements get bigger successive siblings may repeat after longer gap.
In mathematics, a periodic function is one that produces same characteristic value for x and x+p where p is the period of the function:
func ( x ) = func (x+p)
Though not quite same as above, we can say that for each element the period after which its sibling element appears is a function of the element’s atomic number:
p = func (x) where p = period , and x= atomic number
Still abstract, isn’t it? If yes then let us build another analogy, albeit fictional, to help explain ‘periodic’ in the sense of what Mendeleev, Mosley and others scientists meant. In order to build the analogy quickly recal the mystery house from the reading aid for Chapter 4. Each mystery house follows the building /construction rules (the Aufbau’s principle for atom) we have described earlier – one bed room on 1st floor, two bed rooms on 2nd floor, three bed rooms on 3rd floor and son.
Let us say we have families of size 1 to 60 to be accommodated with no two families having same family size. So essentially 60 different families need accommodation.
Now the problem to solve: How often homes with similar room occupancy repeat? To find the answer let us see how families are accommodated:
Answer: 2, 8, 8 , 18, …
The repetition interval/gaps (or shall we say ‘period’) is not same as you can see above with s1 (s room with single occupant). We can ask similar question with respect to s2 (s room with two occupants), p1, p2, ..p6, d1, d2, …, d10, and f1, f2, …f14. We will have similar repetition patterns.
Repetition pattern is what the scientists meant by ‘periodicity’. The gap between two homes (the siblings if you will) of similar bed room occupancy at the outermost energy level. The gap depends on the size of the first house. For example:
street 1: for s1 home on this street, the next s1 house is 2 homes away on 2nd street
street 2: for s1 home on this street, the next s1 home is 8 homes away on 3rd street
street 3: for s1 home on this street, the next s1 home is 8 homes away on 4th street
street 4: for s1 home on this street, the next s1 home is 18 homes away on 5th street
In the example above, we are able to see and justify gap pattern given the bed room occupancy rules we laid out as part of our game for the mystery house. Mendeleev and others of 1870’s didn’t know the inside of elements as much as we do now in terms of atomic model and electron configuration. They only knew external characteristics such as color, reactivity etc of elements. Using such externally known properties they found that elements with similar characteristics repeat at certain intervals. It is only after 30 years , when Bohr and other scientists formulated atomic model , that scientists were able to piece together logical explanation for the periodic pattern 8, 8, 18 etc (see Note 2 for a Hindu myth).
Now that we understand the history behind periodic table , let us see how it is organized and how properties of elements trend across a row (period) and across column (group) of the table.
Section 2: the blocks in periodic table
Section 3: the atomic properties and their trends
- As you will learn later in your science education, ocean waves, after travelling some distance, flatten out. The energy that created the wave slowly drains out as the wave travels further away from the point where it was created as there is no new energy to replenish to keep the wave going. This is similar to how your cell phone battery drains after some use if you don’t charge it again.
- In Hindu mythology and folklore it is often mentioned that Bramha, the creator of life, some times makes seven identical copies each time he creates a new persona (soul) Each copy maintains similar facial , structural and other physical characteristics. The copies may be born to different mothers, in different ages, in different races, in different places. Reincarnation is also an essential part of Hindu psyche. One can be re-born as many as 7 times. Is it purely coincident that there are at most 7 siblings for elements? Or could it be the work of some high order to ensure there are at most 7? Despite its unscientific and irrational nature, the myth might give inspiration to biologists to search for periodicity in human genetics. Could there be Nobel prize prospects for finding ‘Periodic Table of Human Genes’ ?
- Periodic Table of Genetics – Possible? (ellanti.wordpress.com)
- Why is oxygen placed where it’s at on the periodic table (wiki.answers.com)
- Seven types of anxiety (could it be related to 7 elements in a column of periodic table) (livingwithanxiety.com)
This is a reading aid (cheat sheet!) for Chapter 4: Arrangement of Eelectrons in Atoms from Modern Chemistry by Holt, Rinehart, and Winston, a 10th grade Honors Chemistry text book in California.
This reading aid could be useful for any student. It can also be used by parents and teachers looking for alternative ways of explaining atomic model and basic quantum mechanics.
This chapter and preceding chapters tries to explain concepts that Niels Bohr, Pauli, Heisenberg, and others contributed to understanding of atoms in the early 1900s.
When we were in school we didn’t have so many distractions and activities. We would read , re-read as many times as needed, including coming up with analogies, until we can memorize the concepts. Not so with iTunes / Facebook generation kids. They are too busy with their iPhone or with their social network or with after school sports and activities. They don’t have time to read at least once let alone re-read. They are likely to think and talk about Bohr, Pauli and others mentioned in the chapter:
Oh, these dudes of a century ago probably didn’t have anything to do. They invented some stuff. Must have been geeks, crazy, retards. …
Fun aside; kids are likely to find it challenging to read the chapter as the concepts discussed are abstract. Atoms and its tenants – nucleus, protons and electrons are invisible to all of us and talking about them to kids is obviously going to be a challenge.
So, in this blog an unconventional approach will be used to teach the following concepts:
- Bohr’s atomic model
- Heisenberg uncertainty principle
- Hund’s rule
- Aufbau’s principle
- Pauli ‘s Exclusion Principle
- Schrödinger Equation
There is a quiz at the end to help prepare students for their class room unit test.
The unconventional approach uses analogies from our real life that the kids can easily relate to. One could even use characters and concepts from popular movies/shows that kids are familiar with such as Wizard of Oz, Harry Potter . You will see one example where Tempur-Pedic mattress is used in explaining Hund’s rule.
Use of analogies and stories is not necessarily to make kids understand atomic model. It is too complex for their age and even for grown ups. Instead, the objective is to help them memorize the concepts more easily.
First, let us start with recap of some basic concepts that students may have come to memorize already about atom:
Atom and its Tenants
- Atom is the basic building block of matter (like Lego blocks is used to build car, truck, home, etc)
- Each atom contains three types of tenants: protons, neutrons and electrons
- Center of the atom is called nucleus (analogy: biological cell with nucleus)
- Protons and neutrons huddle inside the nucleus
- The number of electrons in an atom is equal to the its atomic number(e.g, Helium has two electrons since its atomic number is two)
Unlike protons and neutrons, which stay inside nucleus as a group of well behaving kids, electrons don’t stick to one place. They are like toddlers. They keep running around inside the atom in spaces called orbitals (also called shells).
Since electron, like a toddler, keeps jumping and moving around, we can’t say, with 100% certainty, where it is or how fast it is moving at any given time. That is what Heisenberg (1901-1976), a German scientist, said almost a century ago: it is difficult to know at the same time where the toddler is and what the toddler is up to because the toddler is unpredictable! The toddler (electron) could be in one place with probability of 1/3, and, at the same time, in another place with probably of ½ and so on. I am sure your mother knew this when you were toddler and you would soon when you have your own kids.
Thus we have the famous Heisenberg’s uncertainty principle for electrons (the toddlers)
it is impossible to know both the exact position and the exact velocity of an electron at the same time
Nobel Prize for ‘No’ answer
Question posed to Heisenberg and team: Can you determine position and speed of electron at the same time?
Their answer: No
Their reward for answering: Nobel Prize in 1932!
So the next time your teacher asks you a science or math question and your response is going to be ‘Don’t know’ then know that you could be in line for Nobel prize!
Joke apart, it is very important to learn to say ‘No’, and how to say it. Saying ‘No’ or ‘Dont know’ requires courage and, more importantly, knowing what you don’t know. Heisenberg and team didn’t just say ‘Don’t know’. They produced scientific explanation of why they Can’t simultaneously determine position and momentum of the quantum particles such as electrons.
Electron’s house and sleeping rules
Like toddlers, electrons wander around inside their home – the atom. But how is their home (atom) organized?
To understand this, imagine a mystery house with multiple floors, rooms and beds. Each bed is laid with head side on north and foot side facing south. Also, each bed can sleep at most two – one on east side and one west side. The occupants of the house are ones with varying level of mystical powers and spells. Some can only stay on the ground floor. Some have enough power to just get to the first level. Some can get upto 2nd floor. Some can go even higher because they have extra spell powers to take them that high. To help easily remember the energry level of electrons, picture characters fromThe Wizard of Oz , Harry Potter and others that exhibit different types of spell powers with varying intensity.
To avoid pillow or fist fights or spell wars, for getting the popular rooms and beds, we will have a simple rule : ones that are less able (i.e with less energy / spell power) are allowed to take lower level floors. Next, smaller rooms shall be taken first before bigger rooms are taken as smaller rooms requiredless power to take. Neils Bohr and Pauli used the term ‘Aufbau’, a german version of this word roughly means building/construction principle. The rule is now commonly called ‘Aufbau’s rule:
electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g. 1s before 2s)
Do you really need Scientists like Bohr and Pauli to tell us how to pick bed rooms in the house? Your parents would have told you that the bed room on the ground is for first two weakest (typically young babies or grand parents or sick ones) and is off-limits for more able members. So to memorize Aufbau’s rule, remember rules for taking floors and bed rooms in the mystery house based on the energy /ability of the individuals involved.
Let us now tabulate the rules for each floor:
Summarizing the order of taking bed rooms (equivalent to order of taking the shells by electrons):
3s 3p 4s 3d
4p 5s 4d
5p 6s 4f 5d
6p 7s 5f 6d
7p 6f 7d 7f
The rule for skipping of 3d and others might be hard to remember. In that case use couple of additional analogies listed in the notes section to help memorize easily.
Long time ago, someone named Hund went into a hotel room with some friends. He noticed that the room had more one bed laid from left to right with entry door being close to the left most bed. To take the right most bed one need to walk from entry door all the way to that bed. So needs more energy to reach the beds farther from the left.
In Hund’s time there were no memory foam or Tempur-Pedic beds. So naturally, he surmised that if two sleep on the same bed then each one when they move in the sleep is going to disturb the other. So he felt that they need to spend extra effort /energy to get some sleep.
Given the two observations from the hotel bed room, Hund laid out the following rule for bed occupancy so that least energy/effort is spent in getting a bed to sleep well:
First person entering the room takes the left most bed. Next person entering takes the next bed and son on until all the beds are occupied by one person each. After that, the next person entering the room pairs up with the one sleeping on the left most bed and so on. See below:
Obviously, we don’t need scientists like Hund to tell us rules on how to pick a bed in a room with multiple beds as it is common sense and we can figure that ourseleves easily. But, electrons, as mystical as they are with varying levels of spell power, do need Hund’s rule to help pick orbitals , the space where they live and move around. Here is what Hund said in scientific terms with respect to sub shell occupancy rules for electron:
When there are multiple sub shells (read beds) in a level (read bed room. e.g 2p), electrons take individual orbitals before they are paired
Take a short Quiz to help you memorize concepts from this chapter. You will get to see your score immediately. You can take the quiz as many times as needed.
Story style explanation of emission spectrum and Schroedinger’s equation (the most complex one) will be in a separate post. They are part of the atmoic model chapter. But worth explaining separately.
- Couple of analogies to help memorize why fill room 4s on 4th floor first while room 3d is vacant on 3rd floor:
- Imagine an expensive hotel with beatiful master suite on 3rd floor. The price to take a bed in the master suite on 3rd floor is way more expensive than taking a bed on the 4th floor. So obviously, electrons prefer 4s compared to 3d as they have to spend less money (energy) to take 4s.
- In monopoly game, you may have to skip a rail road or utility to take the next property available since you don’t have enough money.