Circular Motion

Understanding circular motion is a prerequisite for the  Kepler’s Laws of planetary motion, the physics of planetary and satellite orbits as well as Newton’s theory of gravitation.

Angular velocity:
Worksheet:  Please see this link for a worksheet on angular velocity
Angular Velocity

 

Angular Acceleration is the rate of change of angular Velocity with respect to time. It is a vector quantity. It is denoted by α. The Angular Acceleration Formula is given by:
Angular Acceleration Formula
Note: non-calculus version – replace the “d” s  with delta

Where, ω is the angular velocity and t is the time taken.

Formula for Angular Acceleration
Centripetal acceleration:
Centripetal acceleration is the acceleration that keeps objects moving in a circle.  Using the earth – moon system as an example, the centripetal acceleration which keeps the moon moving a round the earth is due to the gravitational field of the earth.

Centrifugal acceleration

Nuclear Processes

Most of the heavy elements in the universe today originated from the explosive burning of super giant stars.

 

This graphic shows how nuclear material is burned to form heavy elements in a red-giant star such as Betelgeuse near the end of its life.

Betelgeuse-in-Orion

The process of a star exploding is called a super nova.  Elements heavier than Iron appear to have been produced by the explosion of super giant stars early in the life of the universe.

supernova-fusion

With each generation of exploding stars and formation of new stars, the “metalicity” or metal content of the stars increase. The Horsehead nebula is a region in the Milky Way where new stars are being formed from the remnants of exploded stars.Horsehead_Nebula

This nuclear burning process results in many elements which have an imbalance of nucleons ie too many neutrons. These unstable elements decay into more stable states forming all the other elements in the periodic table.

In this lesson, we’ll study nuclear decay and the 3 major kinds of nuclear radiation.

________________________________________________________________

To start with the He nucleus is the most stable of all nuclear building blocks. He has 2 protons and 2 neutrons.

When an unstable nucleus decays by losing a He nucleus it is called Alpha Decay. Alpha decay lowers the atomic number of the parent nucleus by 2 (protons) and lowers the atomic mass by 4 amu (2 protons + 2 neutrons).

Another way that a nucleus can get rid of excess neutrons when a neutron loses a high energy electron and transforms into a proton. This process is called Beta Decay.

The third method of nuclear decay happens when a high energy photon or light particle is emitted. This is called Gamma decay. In Gamma decay, the nucleus loses a large amount of energy. This usually happens when a nucleus splits into two or more parts such as during Alpha Decay.

 

Emission Spectroscopy Lab

Warm up:  Do you think  the emission spectrum of Hydrogen is made of a continuous rainbow of colors or a set of individual colored spectral lines?  Why?

Hint: review your notes and your worksheet on the Hydrogen electronic transmissions, especially the Balmer Series.

These pictures show the difference between continuous, emission and absorption spectra.

Em-Abs-spectra

Why is the absorption spectrum the opposite (compliment) of the emission spectrum?

Study these specra before looking at the spectra from the gas discharge tubes.

 

EmissionSpectra-Hg-H-He

In the space below, draw the emission lines for H, He and Hg using colored pencils.

Hydrogen ________________________________________________________

 

Helium ____________________________________________________________

 

Mercury __________________________________________________________

 

Now look at the emission lines of the gas discharge tubes and put  Czech marks on your drawing  above each spectral line you were able to see.

 

 

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.

Spectroscopy

Spectroscopy is the study of materials based on the wavelength of their reflected or emitted light.

In chemistry, flame spectroscopy is used to identify the elements in an unknown material sample by heating the sample in a flame and observing the color light emitted.  visible-s

Here’s a video that explains how the flame spectrometry lab works…..

Lab: for each sample,  approximate the wavelength of emitted light by finding the corresponding color on this chart. Notice that the wavelengths are given in nanometers.

What is a nanometer?

Then calculate the energy of the emitted light using Plank’s formula;

E = hv = hc/Lambda

where h is Plank’s constant 1.67 x 10^-19 Joules and c is the speed of light 3.0 x 10^8 m/s.

Or use hc = 12,400 eV Angstroms.

Next find the energy levels of each sample element on the resource table and identify which electronic transition is accounting for most of the emitted light.

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.