Chapter 4�Arrangement of Electrons in Atoms

Section 1: The Development of a New Atomic Model

Modern Chemistry (2009) 4:1

5-2020

L. Blanchard Byrne

Target 04-01 I can use historical models of the atom to explain how atoms give off different forms of electromagnetic energy and to explain how electron energy levels can be measured.

How Does a Chemist Determine What Materials are Made of?

How could you tell what elements a star is made of if the only data you can collect is the light coming from it?

If you energize a gas, it gives off a characteristic color of light that when passed through a diffraction grating, breaks into bright lines - emission spectrum.

Where does the emission spectrum come from? Why is it unique to a specific element?

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To answer these questions, we need to understand some concepts about light.

This is the light coming from one star.

Properties of Light

• Is light a particle or a wave?

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Electromagnetic Radiation

• Energy that exhibits wave-like behavior as it travels through space.
• X rays
• Ultraviolet Light
• Microwaves
• Infrared Light
• Visible Light

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Electromagnetic Spectrum 053

Electromagnetic Spectrum 053

Electrons are Wave-Particle Dualities

Electrons are Wave-Particle Dualities

All forms of electromagnetic radiation travel at the same speed - the speed of light (c) = 3.00 x 10⁸ m/s

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c = 𝛌 x 𝝂

speed of light = wavelength x frequency

Practice Problem

Calculate the wavelength of the yellow light emitted by a sodium lamp (those in which you find on street corners) that has a frequency of 5.10 x 10¹⁴ Hz.

𝛌 = c 3.00 x 10⁸ m | sec

𝝂 sec | 5.10 x 10¹⁴ 1

(to divide by a fraction (Hz), invert and multiply)

𝛌 = 5.88 x 10^-7 m

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Photoelectric Effect

What should happen to the amount of electrons released if the intensity of the light is increased?

Electron Energies

What should happen to the quantity of electrons released if the color (frequency) of the light is increased?

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Classical understanding predicted that an increasing amount of electrons would be emitted, red (low frequency) would would produce fewer and blue at the higher frequency would produce more. Every frequency would produce some electrons.

Photoelectric Effect

PhET Simulation

https://phet.colorado.edu/en/simulation/legacy/photoelectric (Requires Java)

set battery to zero and intensity to 100%

Design an experiment to test whether intensity (brightness) has an effect on the number of electrons emitted.

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Design an experiment to test whether color (frequency) has an effect on the number of electrons emitted.

Photoelectric Effect

When light strikes a metal surface, electrons may be ejected causing a current to flow. This process is called the photoelectric effect.

Photoelectric Effect

Each different metal has its own characteristic energy level. When light is not energetic enough it will not eject electrons. Neither the red or the yellow light are energetic enough to eject cesium metal electrons

Photoelectric Effect

Green light is energetic enough and current flows.

E_photon = h ѵ

• A photon is a particle of electromagnetic radiation having zero mass and carrying a quantum of energy.
• A quantum of energy is the minimum quantity of energy that can be lost or gained by an atom.

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• The energy (joules) of a quantum of radiation is equal to Planck’s Constant (Joules times seconds) times the frequency of radiation (Hz or seconds^-1)

h = 6.626 x 10^-34 J s

Electrons are Wave-Particle Dualities

Photoelectric Effect (Albert Einstein 1879 - 1955)

• Conclusion: a beam of light is a package of photons, each with a given amount of energy (E) that depends on the frequency (𝝂) and Planck’s constant (h)
• Different metal electrons are held on with different strengths (intermolecular forces), therefore different metals eject electrons when photons of specific colors (frequencies of light) deliver the minimum necessary energy.
• If threshold frequency was reached, electrons of specific energies were ejected

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E = 𝝂 x h (h = Planck’s constant = 6.62 x 10^-34 J s)

Practice Problem:

What is the energy of a quantum of microwave radiation that has a frequency of 5.62 x 10⁹ Hz?

E = 𝝂 h

E = 5.62 x 10⁹ 1 | 6.626 x 10^-34 J sec

sec |

E = 3.72 x 10^-24 J

Electrons are Wave-Particle Dualities

Practice Problem:

What is the frequency of an ultraviolet quantum if it has an energy content of 1.89 x 10^-16 J?

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E = 𝝂 x h (h = Planck’s constant = 6.62 x 10^-34 J s)

𝝂 = E

h

𝝂 = 1.89 x 10^-16 J |___________________

| 6.626 x 10^-34 J sec

𝝂 = 2.85 x 10¹⁷ sec^-1 or Hz

Hydrogen Gas Excited to Plasma Phase

pHET Interactive Models of the Hydrogen Atom

https://phet.colorado.edu/en/simulation/legacy/hydrogen-atom

Energy of a Photon

Niels Bohr (1885-1962) proposed a model of the atom that quantized the energy states electrons could take around a nucleus. When in the ground state, the atom had a definite fixed energy.

electron at ground state

quantized levels where electrons could be

Energy of a Photon

• An electron can move to a higher energy state by gaining an amount of energy equal to the difference in energy between the orbits.
• When in the excited state, the electron can drop down to a lower energy state by emitting a photon.

electron becomes energized by a photon

electron returns to ground state

Energy of a Photon

The energy of the photon emitted (color) is equal to the difference in energy between the excited state and the ground state of the electron.

Energy of a Photon

If the electron absorbs a photon of E = red and jumps to E₂, what energy will the electron emit when it returns to ground state?

If a photon of E = green is emitted, what energy did the electron receive in order to get to E₃?

Energy Levels and Emission Lines

Infrared Light

Visible Light

Ultraviolet Light

Energy of a Photon

Energy of a Photon

93.7 MHz is a common radio frequency. What is the energy of the photons at this frequency?

Energy of a Photon

10-26J

Energy of a Photon

How energetic is blue light compared to red light?

Why do some colors (frequencies) have enough energy to trigger the photoelectric effect?

Electrons are Wave-Particle Dualities

Double-Slit Experiment

• a light source is passed through a plate with 2 parallel slits – the pattern produced is observed on a screen
• Results:
• Wave Nature of Light
• light waves pass through and interfere (constructive & destructive) on the other side producing light and dark bands on the screen
• Particle Nature of Light
• the light is absorbed on the screen as distinct points or individual particles
• detectors at slits found that each photon only passes through one slit (if it was a wave, would pass through both)

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What if we release one electron at a time?

Expected Outcome

Achieved Outcome

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Where do the colors come from?

A quantum of light is emitted when an electron drops to a lower energy level.

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Ground state is the lowest possible energy level of the electron (n = 1).

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atomic emission spectrum: the spectrum formed when light passes through a prism that separates it into its different frequencies

• sunlight is a mixture of ALL visible light frequencies

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• the light emitted by atoms consists of a mixture of specific frequencies
• no two elements have the same emission spectrum - produced

So… What is our star made of?

How might could this information be used to explain the colors in fireworks?

Is light a Wave or Particle?

Is light a Wave or Particle?

Is light a Wave or Particle?

Is light a Wave or Particle?

Is light a Wave or Particle?

Is light a Wave or Particle?

Fin