Category Archives: Physical Science Unit 1: Atoms

Physical Science Unit 1 presentations

The Scientific Method (not in textbook)

Measurements and Sig Figs (not in textbook)

What Is Chemistry?: Textbook Section 12.1

Intro To Chemistry Part 2: Atoms and Elements: Textbook 12.1-12.3

Atoms And Elements: Textbook Section 12.2-12.3

The Periodic Table: Textbook Section 12.4

Isotopes (not from textbook)

Atoms, Elements and Isotopes

The Shell Model: Textbook Section 12.9

History of the Atom

 

Where Oh Where –  did all these atoms come from?

All the atoms we have today were created as a result of the Big Bang in the early days of the universe.  As the Early Universe cooled,  protons and electrons formed and joined together to form Hydrogen atoms.  Later, stars formed and “burned” the Hydrogen producing Helium.  Larger, hotter stars continued to burn the Helium to produce heavier atoms such as Iron and Magnesium, then exploded, spewing meals (iron, magnesium etc) across the universe. These metals together with Hydrogen and Helium are the materials which stars, planets, and galaxies are made of.

How did we come up with today’s  models of the atom?

It all started with Democritus.

democritus

Democritus was a great and wise Greek philosopher who lived from 460 BC to 370 BC.  Plato hated him but Democritus had a great sense of humor which undoubtedly irritated the serious Plato (428 BC – 328 BC) even more.  He went blind in his old age and lived till 90,  although some historians believed he lived to 109! Most of his writings were destroyed in th middle ages so his life has become filled with legend.

Democritus’ theory of atoms started as a thought experiment. He (in discussion with Leartus) said if you divide a grape in half and in half again and keep dividing it, eventually you will reach the point where you can divide it no more.  He called these smallest possible pieces “atoms” which meant indivisible in ancient greek. He also believed there was empty space or “void” between the atoms.

Later Aristotle, (384 BC-322 BC) disagreed with Democritus’ theory since he knew that nature could not allow a “void”. Aristotle believed that matter was made from the 4 elements of the ancients; earth, air, water, and fire. Today we know that Democritus was closer to the truth than Aristotle. The problem was, Aristotle was so famous that everyone believed him, setting science back 1,000 years.

father-time   Fast Forward to the late 1700’s

By the 1700’s, scientists had figured out that there were 2 kinds of electric charge. Opposite charges attracted one another. Like charges repelled.  Benjamin Franklin, one of our nations founding fathers, was fascinated by these electric charges. He deemed he could capture the power of electric lightning  by flying a kite with a metal key on the string. He was right, and the result was shocking!

ben_franklin50

Benjamin Franklin was the first to name the opposite charges plus +, andfather-time.jpeg minus -. He also invented the lightning rod.

In 1803, John Dalton, extended the ideas of Democritus. Dalton reasoned that all atoms of a specific element were identical and in some way different from the atoms of other elements.

father-time

In the late 1800’s scientists were busy trying to understand the structure of atoms.
In 1897, J.J. Thomson, using cathode ray tubes, identified the electron. Thomson went on to propose a model of the atom called the Plum Pudding model. He pictured the atom as being a ball of positive charge with negative electrons stuck in it, the electrons being much like the pieces of plum in plum pudding, a popular British desert.

plum-pudding  Thomsons plum pudding model

In 1911, Ernest Rutherford designed an experiment using a thin gold foil and a beam of Alpha Particles (Helium nuclei). Rutherford was hoping to confirm Thomson’s model. He expected the beam of Alphas to pass through the gold with only minor spreading of the beam. What he found instead was that some of the Alpha particles were “scattered” through wide angles, some even bounced straight back. This set the scientific community on its head and they soon discarded the now stale plum pudding model.

Rutherfords-experiment

 

Rutherford Scattering

Click to Run

 

The Bohr Model

In atomic physics, the Rutherford–Bohr model or Bohr model, introduced by Niels Bohr in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar in structure to the solar system, but with attraction provided by electrostatic forces rather than gravity.

bohr_hydrogen

Bohr defined the “orbitals” as having primary quantum numbers n = 1, 2, 3, etc.

bohrplanetarymodel

Looking back to the spectral lines we saw in the gas discharge tube demonstration, we see that electrons were excited to a higher n quantum level by the power supply. Then the electrons returned to their ground state by releasing energy in form of “photons of light” where the photon energy or color can only have specific values (colors).

h-emission

 

bohr-atom-transitions

various-emission-spectra

Assessment: Why do different elements have different emission spectra?

Hydrogen Emission Spectra

LO: Understand how Hydrogen’s electron energy levels result in the Hydrogen emission spectra.

As we studied yesterday, the Bohr model describes the energy levels of an atom as a series of shells with the the inner shell being at the lpwest or ground state energy.

Here’s a graphic of Hydrogen’s energy levels, the electronic transitions between levels, the Lyman, Balmer, and Paschen series.

(thanks to: “Hydrogen transitions” by A_hidrogen_szinkepei.jpg: User:Szdoriderivative work: OrangeDog (talk • contribs) – A_hidrogen_szinkepei.jpg. Licensed under CC BY 2.5 via Commons – https://commons.wikimedia.org/wiki/File:Hydrogen_transitions.svg#/media/File:Hydrogen_transitions.svg )

Hydrogen-Emission-Lines

Make a table with 3 columns.

Column 1: write the wavelengths of the Balmer series transitions.

Column 2: For each, write the transition from n’  to n.

Column 3: For each transition, use the wavelength to identify the color of the emission line. (hint, reference the visible spectrum in your book or use the following spectrum;

visible-s

Q: Which emission line has the most energy, which has the least energy.

Periodic Table: Orbitals

Learning Objective: to understand the order in which electrons fill orbitals and how the orbitals are arranged in the periodic table.

In your notebooks, sketch the 1s, 2s and 2p orbitals.

Now sketch this graphic.

orbital-blocks

Now with a ruler, draw in columns for Groups I – VIII. Use the periodic table on the wall or in your book for reference.

There are some real mysteries here. Notice that the 3d orbitals are actually part of row 4 of the periodic table. The reason for this is that the orbitals fill in a very special order.

Copy this chart to your notes:

electron_orbital_filling_chart1308104179633

Conclusion: The 1s fills first. Then the 2s, then the 2p then the 3s, then the 3p. Note the4s fills before the 3d, 4p and 5s.
Next step: How may electrons can an s orbital hold? _____________  Why? ________
How many electrons can a set of p orbital hold? _______________   Why?________

Why do orbitals fill in such a weird order?
The answer has to do with the specific energies of the orbitals – and YES – there is definitely some overlap.

The principle that orbitals fill up according to their energy is called the “Aufbrau Principle”. In fact the lowest energy orbital (1S) is always the first to fill.

Here’s a plot of the orbits and their energy levels….

 

aufbaudgrm

Notice that the 4S orbital has a lower energy than the 3 d orbital – this means that the 4s orbital will fill with electrons before the 3d orbitals start to fill (K, Ca).

The electron configuration of an element is simply a list of which orbitals have electrons in them and how many electrons are in each orbital.

Examples: Hydrogen 1S1

Carbon  1S2, 2S2, 2P2

Class Project:
1] Now write a list of the first 20 elements by symbol (name).
2] For each element, draw a pyramid diagram to figure out the order in which the orbitals fill.
3]Write down the electron configuration for each of these 20 elements.
and write the electron configuration for each element.

Conclusion: You can now write the electron configuration for any element.

Isotopes, Atomic Weights and Abundances

isotopes-and-abundances-2Isotopes:
An isotope is a variation of an element which has more or fewer neutrons while having the same number of protons. Remember, it is the number of protons which define the number of electrons and therefore define the element’s chemical properties. Some of an elements isotopes may be unstable and one of the excess neutrons can decay into a proton plus an energetic electron (Beta emission). Carbon 14 is a radioactive isotope of Carbon 12 and is used to determine the age of fossils.

Watch this video then draw the nucleus of Carbon 12 and the nucleus of Carbon 14.

Here are some practice problems to help you understand atomic number and atomic mass of isotopes.

isotope-practice-worksheet-1

Abundances:

Since several isotopes of an element may occur naturally in nature, we need to examine how the isotopes mix to give us the correct atomic weight.

Th first step is to understand “abundance”. Abundance is a number that tells us how common one particular isotope is.  Abundances are  usually expressed in percent or in parts per million or as a decimal.

The next thing to understand is that atomic weights are measured in AMU’s or Atomic Mass Units. 1 AMU is 1/12th the weight of a Carbon 12 nucleus. Carbon 12 has 6 protons and 6 neutrons.

Example:  The abundance of Europium  151 is 48.03% and the abundance of Europium 153 is 51.97%.

Step 1: convert % to decimals.
Eu 151:   48.03%  = 0.4803
Eu 153:   51.97% = 0.5197

Step 2:  Now multiply the atomic weight of each isotope times its abundance.
Eu 151:   151 AMU x  0.4803  = 72.53 AMU
Eu 153:   153 AMU x  0.5197 = 79.51 AMU

Step 3:  Add these numbers together to get the average atomic weight of Europium

72.53 AMU  + 79.51 AMU = 152.0 AMU

The following worksheet provides lots of practice for calculating atomic weights.

isotopes-and-abundances-2

Now let’s talk about how Carbon dating is used. Watch the first 2 minutes of this video, then answer the question.

Assume Carbon 14 is created at a constant rate in the upper atmosphere. Knowing that the amount of Carbon 12 is constant while Carbon 14 decays, how long will it take for the amount of Carbon 14 in a dead animal such as a dinosaur to reduce to half its original amount.

Explain how Carbon 14 is used to determine the age of fossils.

 

How do we know isotopes actually exist ?

Elements can be separated into isotopes using a  mass spectrometer.

mass-spectrometer_3 mass_spectrometer_2The material to be analyzed is placed in a crucible inside the vacuum system. A beam of electrons heats the saple till it starts to vaporize.  The vaporized gas atoms are then ionized, accelerated through an electrostatic potential (Voltage). then separated using a magnetic field.

The number of atoms detected along each path is used to

mass-spectrometer-4determine the Isotopic Abundance of each species.

 

Atomic Structure: Orbitals

Learning Objective:  To understand how electrons are configured in atoms.

Rule 1: For neutral atoms (ie not ions) the number of electrons equals the number of protons. This results in equal numbers of + proton and – electron charges for a net charge of 0.

Rule 2: Electrons are held in very specific ways in shells and each shell is composed of orbital orbitals. Each orbital can contain up to 2 electrons (these electrons are paired spin up and spin down – we’ll discuss spin later).

Rule 3: Each row of the periodic table describes the outer shell or valence electrons. The shells are defined by “principal quantum numbers” as n=1, n=2, n=3 etc. The first row of the periodic table is n=1, the second row n=2 etc.

The following table shows the shell and the number of electrons it can hold.

n=1  2 electrons

n=2  8 electrons

n=3  18 electrons

n=4  32 electrons

What do orbitals look like?

Do now: We’ll replay the video. Draw the 1S, then separately 1S and 2S, and 1S, 2S and 2P orbitals.

Now to understand quantum numbers:

There’s a subtlety here in that the order in which the shells are filled is mixed so the 4s orbital fills before the 3d orbital is filled We’ll learn more about this when we study the Aufbrau Principle.

Rutherford’s Model of the atom

Rutherford’s Experiment (animation)

Crash Course: The history of atomic theory

 

 

Assignment:  Write a 1 page (minimum) essay on the history of the atomic theory. Include a timeline of the 3 most important scientific discoveries that led to Rutherford’s experiment and identify the scientists or philosophers who made these contributions.

Describe Rutherford’s experiment – this can be in words or an annotated diagram. Describe what Rutherford expected to find and why (what model of the atom was Rutherford trying demonstrate?)  Describe what Rutherford actually observed.  State Rutherford’s conclusion and discuss how Rutherford’s model of the atom is supported by his experimental results.

This essay may be hand written or printed or typed.

Significant Figures & Precision

Learning Objective: to understand the meaning of significant figures, to be able to calculate numbers to the correct significance, and to understand how significant figures relate to the precision of a measurement.

Precision: I asked my students how old they were and their answers ranged from 15 to 16. One student said 15 and a half, another said “I’m almost 16”. Much to my surprise, no one answered “I’m 15 years, 2 months, 4 days, 17 hours, 18 minutes and 43 – no wait – 44 seconds old”!  The question to ask is how large or small a quantity do you need to properly represent something. In most conversations, saying you are 15 or 16 is good enough. We could say that you approximate your age to the last full year.  So the degree of precision is 1 year. You’re either 15 or 16 – that’s it. To be more precise, you might say that you are 15 and 1/2. Then the degree of precision would be 1/2 year. You can keep getting more and more precise to months, days, hours and seconds or even to 1/1000ths of a second.  This would be a very high degree of precision to be sure.

How does precision affect mathematical calculations?

The least precise measurement or number determines the overall precision of a calculation.

Consider the number 3. Is 3 really the same as 3.0?  The answer is that you don’t have enough information to tell for sure.  In fact the number 3 actually represents any number from 2.5 to 3.4999… which has been rounded to the nearest integer. 2.5 rounds up to 3 as does 2.6, 2.7, 2.8, and 2.9.  3.1 rounds down to 3 as does 3.2, 3.3 etc. right up through 3.4.

Now for a more difficult problem.  Is 3×3 the same as 9?

The smallest possible value for 3 could be 2.5.                                      2.5×2.5 = 6.25 rounds down to 6.                                                                       The maximum value of 3 could be 3.4999.                                                             3.4999 x3.4999  =  12.                                                                                             Take the average of these results (6 + 12) / 2 = 18/2 =9.

 

 

 

Orders of Magnitude aka Powers of 10

Learning objective: To understand powers of 10,  know how to multiply and divide powers of 10, and know how to convert from decimal to scientific and engineering notation.

Part 1: What are Orders of Magnitude and powers of 10?
So you’re sitting at coffee shop and some Physicists are writing order of magnitude calculations on the back of an envelope. You want to listen in and comment on the discussion but first you need to understand what they’re talking about.  This post is a simple study guide to help you understand and use powers of 10 and orders of magnitude.

First some simple definitions;

Decimal notation:  3.14159 ie numbers and a decimal point. More examples: 73,015.238,  1.059,  0.00063 etc.

Scientific notation: a decimal number between 1.0 and 9.999… multiplied by 10 raised to some power (also called an exponent).     scientific notation examples: 6.022×10^23 (Avogadro’s number), 1×10^100 a 1 followed by 100 zeros also known as 1 google, 1.602×10^-19 the charge of an electron, 6.67×10-11 the gravitational constant………. and the list goes on. Notice that the carrot “^” in 10^23 means 10 is raised to the 23rd power. This is the same as saying 1 followed by 23 zeros.  Formally, the correct way to write a number in scientific notation is 10 with the exponent written as a superscript but this is less common today because it’s easier to type ^ than to make a superscript.

Exponential notation: same as scientific notation

Engineering notation: Engineers started typing equations a long time ago, there was no “^” key on most of the old typewriters so engineers simply used the letter “e” or “E” to mean exponential notation.  For example, 6.022×10^23 could be written as 6.022e23 or as 6.022E23.  Negative exponents work the same way so 1.062×10^-19 = 1.062e-19 = 1.062E-19.

Order of magnitude: the exponent only, note round the number part down to 1 or up to 10 and adjust the exponent.                    examples: 1.062×10^-19, 1.062 rounds down to 1×10^-19 so the order of magnitude is -19 while 6.022×10^23 rounds up to 10×10^23 = 1×10^24 has an order of magnitude of 24.

Simple! Right?

 

But what do these numbers – powers of 10 or orders of magnitude really mean?

Let’s watch the following 1-1/2 minute video to see how these numbers relate to the real world.

Here’s another, more detailed video with explanations. Please watch this video for homework. Answer all the questions following the video.

Questions:1] What is the order of magnitude of the size of;
a] our galaxy
b] the Earth
c] a plant cell
d] the width of a DNA molecule
e] an atom
f] the nucleus of an atom

Part 2: How to calculate using powers of 10

Multiplication is really simple. All you do is add the exponents.
examples;
10^6 x 10^7 = 10^13 (add exponents 6 + 7 = 13)
For negative exponents you still just add but don’t lose the minus signs.
example: 10^4 x 10^-6 = 10^-2 (add exponents 4 + (-6) = 4-6 = -2)

Dividing works the same way except that your bring the power of 10 in the denominator up to the numerator and change its sign. Formally, this is the same as multiplying top and bottom with the power of 10 with its sign changed (reciprocal).

example:  (10^4)/(10^6) =  (10^4)/(10^6) x (10^-6)/(10^-6)

= (10^4 x 10-6)/(10^6 x 10^-6)

numerator: (10^4 x 10-6) =  10^-2

denominator: (10^6 x 10^-6) = 10^(6-6) = 10^0 = 1

So the answer is 10^-2  – in decimal notation this is 0.01

Now do these problems:

a] 10^2 x 10-^2 = ?

b] 10^2 x 10 ^8 =?

c] 10^7 x 10^8 =?

d] 10^-7 x 10^8 =?

e] 10^7 x 10^-8 =?

f] 10^7 / 10^8 =?

g] 10^1 / 10^8 =?

h] 10^0 /10^8 =?

i] 1/ 10^8 =?

Next Lesson: Significant Figures