Site hosted by Angelfire.com: Build your free website today!

The International School of Panama

General Chemistry Notes: Chapter 5

Electrons in Atoms

Light and Quantized Energy

Two questions Rutherford’s model of the atom could not answer:

· Why the negative electrons are not pulled into the atom’s positive nucleus…

· Why do different elements have different chemical behavior…

Wave Nature if Light

http://imagers.gsfc.nasa.gov/ems/waves3.html

Wavelength (l) : is the shortest distance between two consecutive equivalent points on a continuous wave (for example between two crests of between two troughs).

http://imagine.gsfc.nasa.gov/docs/teachers/lessons/roygbiv/roygbiv.html

Frequency (n) : The number of waves that pass a given point per second. The SI unit for frequency is the Hertz (Hz)

1Hz = 1 wave per second =_1_ = s^-1

http://imagine.gsfc.nasa.gov/docs/teachers/lessons/roygbiv/roygbiv.html

Amplitude: the wave’s height from the origin to a crest or from the origin to a trough.

http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l2a.html#amplitude

Electromagnetic Radiation: a form of energy that exhibits wavelike properties and travels through space at the speed of light.

The electromagnetic spectrum (EM) encompasses all types of electromagnetic radiation, with the only difference being the frequencies and wavelengths.

http://amazing-space.stsci.edu/resources/explorations/light/ems-frames.html

http://imagers.gsfc.nasa.gov/ems/visible.html

Order of the Color: ROY G BIV

Speed of light: c= 3.00 x 10⁸ m/s

The frequency and the wavelength are inversely proportional: The longer the wavelength the smaller the frequency.

n = c_

The waves with shorter wavelength are more energetic. Violet is more energetic than red. Ultraviolet light is more energetic than infrared.

Sunlight and in general white line contains all the colors of visible light. When white light is passed through a prism, is separated into a continuous spectrum of colors:

http://can-do.com/uci/ssi2001/emspectrum.html

Problem:

Microwaves are used to transmit information. What is the wavelength of a microwave having a frequency of 3.44 x 10⁹Hz?

n = c_ à l= c_à l= 3.0 x 10⁸m/s = 8.72 x 10^-2m

l n 3.44 x 10⁹1/s

Do problems 1 to 5 p. 121

Particle Nature of Light

The wave model of light cannot explain why heated objects emit only certain frequencies of light at a given temperature.

1900, the German Physicist Max Plank began investigating this as he studied the light emitted from heated objects.

His conclusion was that matter can only gain or lose energy in specific amounts multiples of small amounts called quanta. A quantum is the minimum amount of energy that can be gained or lost by an atom.

Mathematically : E _quantum = hn

h= Plank’s constant = 6.626 x 10 ^–34J.s

This explains why the energy of UV light is greater than the energy of IR light. (UV has greater frequency)

Later, in 1905, Albert Einstein proposed that electromagnetic radiation has both properties of particles and properties of light. This is known as the dual behavior of light. He called these particles photons. Extending on Plank’s idea he said that the energy of the photons is E _photon = hn

Problem. What is the energy of a photon from the violet portion of the rainbow if it has a frequency of 7.23 x 10¹⁴ s^-1?

E _photon = hn

E _photon = 6.626 x 10 ^–34J.s x 7.23 x 10¹⁴ s^-1= 4.79 x 10^-19J

Do problems 5 and 6, p. 124

Atomic Emission Spectra

When elements are heated, or provided other forms of energy, until they emit light; if this light is passed through a prism, instead of continuous spectra containing all the colors, line spectra with specific lines of colors are observed. This type of spectrum is called emission spectrum or bright line spectrum.

http://www.iun.edu/~cpanhd/C101webnotes/modern-atomic-theory/emission-spectrum.html

The lines shown are specific for each element and each element gives always the same line spectrum That is why the line spectra are like the fingerprints of the element and therefore they can be used to identify the elements.

Enter this site to see other emission spectra:

http://home.achilles.net/~jtalbot/data/elements/

Quantum Theory

Bohr Model of the Atom

In 1913, Niels Bohr proposed a quantum model for the atom that explained the emission spectra of the elements. He said that the electrons are around the nucleus, like the planets around the sun, in circular orbits of certain energy. He said that the closest to the nucleus, the lower the energy of the orbit. Bohr’s model predicted the frequencies of the lines in hydrogen’s emission spectrum. Building on Plank’s and Einstein idea of Quantized (only certain values are allowed) energy, Bohr proposed that the hydrogen atom has only certain allowable energy states. The lowest allowable energy state of an atom is its ground state.

http://theory.uwinnipeg.ca/mod_tech/node152.html http://theory.uwinnipeg.ca/mod_tech/node151.html

When the atom gains energy and the electrons jump to higher levels of energy the atom is an excited state. The electrons tend to go back to their ground state and emit energy of certain frequencies. These emissions of energy of specific frequencies explain the specific lines observed in the bright line or emission spectra.

Good points about Bohr’s model:

1. He used Plank and Einstein’s conclusions about Quantized energy

2. He explained the hydrogen emission spectrum

3. He calculated very accurately the different energy levels

available for the single electron in the hydrogen atom.

4. He predicted the existence of lines in the UV and IR regions that were later discovered.

http://theory.uwinnipeg.ca/mod_tech/node151.html

However, Bohr’s model couldn’t explain the spectrum of any other element. Why?

Because Bohr’s model was fundamentally incorrect.

We know today that the electrons are not in specific orbits and don’t follow and specific path.

The Quantum Mechanical Model of the Atom also known as the Wave Mechanical Model of the Atom or simply Wave Model.

In 1942, Louis De Broglie proposed that in the same way as light can behave as waves and particles, particles also can also show a dual behavior. They can have characteristics of particles and waves. In other words, he predicted that all moving particles not only behave as particles but also as waves.

De Broglie’s equation for the wavelength (l) of a particle of mass (m), moving at velocity (v):

l = h

m v

For the very small particles like photons, the behavior is predominately of waves. For very large particles, like a baseball, the behavior is predominately of particles. But for intermediate particles, like the electrons, the behavior shows clearly both characteristics, waves and particles’ characteristics.

Heisenberg Uncertainty Principle

If you try to measure the position and velocity of a moving object, you affect its position or velocity.

Heisenberg Uncertainty Principle: It is impossible to know the position and velocity of a particle at the same time. For large particles this uncertainty is not important, but for small particles like the electrons, moving constantly and randomly around the nucleus, the uncertainty is even larger than the diameter of the atom they move in.

Erwin Schrödinger, treated the electron in the hydrogen atom as waves and derived equations, based on the mathematics of waves that not only could be applied to the hydrogen atom, but also the atoms of other elements. This model is known as the quantum mechanical model, wave mechanical model or wave model of the atom.

In this model, instead of trying to describe an specific path for the electrons (like Bohr’s model) the wave function describes the probability of finding the electron in a given area of the space.

So instead of orbits, we describe ORBITALS (atomic orbitals).

An orbital is the region in the space where a given electron is most likely to be found. Each orbital is like a cloud with areas with more or less density depending on the greater or smaller probability of finding the electron.

Examples: These clouds show the probability distribution of certain orbitals… They don’t have an specific boundary, but they represent the region were the given electron(s) have 95% probability of being there.

http://www.chemguide.co.uk/basicorg/bonding/orbitals.html

To describe the position of each electron in the atom, the wave function assign 4 quantum numbers (n, l, m_l and m_s) that describe the relative sizes and energy level of orbitals, type of orbital (shape), orientation of the orbital and the spin of the electron.

An atom has levels and sublevels of energy.

The first quantum number n is called the principal quantum number. It describes the atom’s major energy levels. As n increases the orbital becomes larger, the electrons spend more time farther from the nucleus and the lever of energy is higher.

The hydrogen atom has only 1 electron. In its ground state the electron occupies the an orbital with n=1. When it’s excited it can jump to orbitals with n= 2, 3, 4, 5, 6 or 7….

The first energy level (n = 1) consists of only one sublevel, the second (n=2) 2 sublevels, the third (n=3) 3 sublevels and so on….Sublevels are named s, p, d or f according to the shape (second quantum number).

All s orbitals are spherical