atomic physicssection 1 © houghton mifflin harcourt publishing company preview section 1...

Atomic Physics Section 1

© Houghton Mifflin Harcourt Publishing Company

Preview

Section 1 Quantization of Energy

Section 2 Models of the Atom

Section 3 Quantum Mechanics



The student is expected to:TEKS

8A describe the photoelectric effect and the dual

nature of light



What do you think?

• Albert Einstein, while working as a Swiss patent clerk in 1905, submitted three papers for publication. The topics for the three papers were: • (1) the special theory of relativity, including E = mc2

• (2) an explanation of Brownian motion• (3) a quantum theory of light used to explain the photoelectric

effect

• Sixteen years later he was awarded the Nobel Prize in Physics for one of these papers.• Which paper earned him this award?



Blackbody Radiation

• A blackbody is a perfect absorber and perfect emitter of radiation.– All radiation passing

through the hole is trapped by multiple reflections and very little is emitted.

– Called a blackbody– When you look into the

hole, it is black because no light escapes.



Blackbody Radiation

• The radiation that escapes a blackbody has a wide range of wavelengths.

• At higher temperatures, the shorter wavelengths such as visible and UV light become more prominent.



Failure of Classical Wave Theory

• The wavelength distribution predicted by classical wave theory was wrong.

• Max Planck proposed a theory that matched the radiation curve.– Energy is given off in

discrete amounts of energy.

– Each unit of light energy is called a quanta.



Planck’s Quantum Theory

• Energy can only be absorbed or released in multiples of a specific value:

E = nhf– h is Planck’s constant (6.63 10-34 J•s)– f is the frequency– n represents the multiple (1,2,3,…….)



Planck’s Quantum Theory

• The energy absorbed or released must always be a whole number multiple of hf.

• A unit of energy used for extremely small values is the electron volt (eV).– The amount of energy an electron gains when

changing its potential difference by 1.0 V– 1 eV = 1.60 10-19 J



Click below to watch the Visual Concept.

Visual Concept

Blackbody Radiation and the Ultraviolet Catastrophe



Classroom Practice Problem

• Find the energy of a photon of green light with a frequency of 5.50 1014 Hz . Give your answer in joules and in electron volts.

• Answer:– 3.65 10-19 J or 2.28 eV



The Photoelectric Effect

• When light strikes a metal surface, electrons may be ejected.

• To escape from the binding forces of the atoms, electrons must absorb enough energy from the light.

• Classical wave theory did not predict the experimental results.



Photoelectric Effect




• Einstein theorized that light was quantized.– Photons, not waves– E = hf

• Based on this theory, either the frequency (or energy) of the photons was high enough to eject the electrons, or it wasn’t.– If energy (hf) was not high enough, no electrons

would escape no matter how intense the light or how much time the light shined on the metal.




Visual Concept





• Work function is the minimum energy needed to escape the metal’s surface.– Some electrons require more than this

minimum.– Any additional energy above hft is the

KE the electron has after ejection.




• Einstein’s photon theory explains the photoelectric effect.– No matter how bright the light (more photons), no

electrons are emitted unless the photons have enough energy (hft).

– A brighter light produces more electrons because more photons strike the surface, but the maximum KE of the electrons does not change.

– Electrons are emitted almost instantaneously because each photon ejects a single electron.




The Dual Nature of Light

Visual Concept



Compton Scattering

• If light has particle-like properties, it could collide with electrons and lose some energy.– Like billiard balls

• The scattered photon has less energy (E = hf), so the wavelength is greater.– The wavelength change is

called the Compton shift.




Visual Concept

Compton Shift



Now what do you think?

• In science, theories are developed and tested. When a theory fails to match the results of experiments, the theory must be modified. • In what ways did the wave theory fail to explain the

ejection of electrons from a metal surface when it was illuminated with light of various wavelengths?

• How did Einstein’s explanation of the photoelectric effect change our ideas about light and also explain the experimental results?




2C know that scientific theories are based on natural and

physical phenomena and are capable of being tested by

multiple independent researchers. Unlike hypotheses,

scientific theories are well-established and highly-reliable

explanations, but may be subject to change as new areas

of science and new technologies are developed

3D explain the impacts of the scientific contributions of a

variety of historical and contemporary scientists on

scientific thought and society

8B compare and explain the emission spectra produced by

various atoms



What do you think?

• Describe an atom. Consider the following in your explanation:• What are the component parts of an atom?

• How do they compare in size?• How does the charge on each compare? • Where are these parts located in the atom?

• Do the component parts of an atom move about or remain in fixed positions?• If they move, describe the motion.



Models of the Atom

• The earliest models described atoms as tiny, indestructible, neutral spheres.

• J.J. Thomson discovered electrons in 1897.– Since atoms had negatively

charged electrons, they must have an equal positive charge of some sort.

• Thomson’s model is like seeds (electrons) in watermelon (positive charge).



Ernest Rutherford

• Rutherford fired positive alpha particles at a thin sheet of gold foil.– Most passed straight through the foil.– Some were deflected as shown.– Thomson’s spheres of + charge would not cause this much

deflection.




Visual Concept

Rutherford's Gold Foil Experiment



Rutherford’s Atom

• A small, positively-charged core called the nucleus

• Mostly empty space outside the nucleus• Electrons circle the nucleus like planets around

the sun.– There was a problem with the electron motion in this

model:• A circling charged particle is accelerating and would radiate

energy, and would spiral into the nucleus as it lost energy.• Atoms could not exist in this model for more than one-

billionth of a second.



Atomic Spectra

• The specific wavelengths of light given off when an electric current passes through a gas– Every element produces different spectral lines.– Rutherford’s model could not explain this phenomenon.



Atomic Spectra



Atomic Spectra

• Emission spectra are the colors given off by the gas.• When white light passes through hydrogen, it absorbs

the same frequencies.– Absorption spectra are used to study gases surrounding the

stars.



Niels Bohr’s Model of the Atom

• Bohr’s model assumed that the orbits of electrons were quantized.– Electrons existed only in certain

energy levels.– Ground state is the lowest level.– Electrons absorb energy and move

to excited states.– They release the energy when

returning to ground state.



Hydrogen’s Spectrum Explained

• The visible lines in hydrogen’s spectrum result from jumps to level 2 from levels 6, 5, 4 and 3.

• Would drops to level 1 produce photons with more or less energy?

• Where would these spectral lines appear in the spectrum?




Visual Concept

Bohr Model of the Atom



Classroom Practice Problems

• The five lowest energy levels for Hg vapor are shown above. Assume an electron falls from E5 to E2.

• What amount of energy is given off in eV and in joules?

• What is the frequency of this photon?

• Is this photon in the visible spectrum?

• Answers:– 2.01 eV, 3.22 10-19 J– 4.86 1014 Hz, visible



Bohr’s Model of the Atom

• Bohr’s model was the first to explain spectral lines, but it raised some questions as well.– It could not be extended well to multi-electron atoms.– It did not explain why electrons did not radiate energy

as they circled the nucleus.– It did not explain why electrons had only certain stable

orbits and other orbits did not exist.




• Describe an atom. Consider the following in your explanation.• What are the component parts of an atom?

• How do they compare in size?• How does the charge on each compare? • Where are these parts located in the atom?

• Do the component parts of an atom move about or remain in fixed positions?• If they move, describe the motion.




3D explain the impacts of the scientific contributions

of a variety of historical and contemporary scientists

on scientific thought and society

8A describe the photoelectric effect and the dual

nature of light



What do you think?

• The photoelectric effect shows that electromagnetic waves can act like particles. Does it seem possible that particles such as bullets or electrons can show wavelike behavior?• If hundreds of baseballs pass through a doorway, will

they spread out like a sound wave?• Will a beam of electrons going through a small

opening diffract?• After splitting a beam of electrons, could an electron

from one beam interfere constructively with one from the other beam?



Wave-Particle Duality• Low-frequency photons (radio waves) have very little

energy.– Energy values (E = hf) are about 10-27 J.

• Too small to detect single photons

• A large number of photons/second are needed

• Behaves more like a wave of photons

• Visible light photons have enough energy to be detected in some experiments, like the photoelectric effect.

• High-frequency photons such as gamma rays behave more like particles.– Wave properties (diffraction, interference) are hard to observe.



Matter Waves

• Louis de Broglie hypothesized that, if light could behave like particles, then particles could behave like waves.– All forms of matter have wavelike properties.– He derived an equation for the wavelength ().



Matter Waves• De Broglie postulated that Planck’s equation could be

used to find the frequency of matter waves.

• De Broglie wavelengths and frequencies for matter waves depend on momentum (mv) and energy (E).



Matter Waves

• Light waves passing through an opening exhibit interference.

• Interference, a wave property, was demonstrated with electrons passing through a crystal of nickel years after De Broglie’s prediction.– The spacing between nickel atoms was about the same as the

wavelength of the electrons.



Classroom Practice Problems

• Calculate the De Broglie wavelength of an electron moving at a speed of 8.0 106 m/s.– Answer: 9.1 10-11 m

• Calculate the De Broglie wavelength for a 0.145 kg fastball thrown at 40.0 m/s.– Answer: 1.14 10-34 m



De Broglie Waves in Atoms

• Electrons in atomic orbits behave like waves and set up standing waves around each orbital.

• Only certain multiples are possible.– Just like standing waves on a string




Visual Concept

De Broglie and the Wave-Particle Nature of Electrons



The Uncertainty Principle

• Heisenberg’s uncertainty principle states that it is impossible to simultaneously determine a particle’s position and momentum with infinite accuracy.– Measuring one of the quantities alters the other one.– For example, measuring the position of an electron

requires that photons bounce off the electron so we can see it. However, the photon striking the electron will change the electron’s momentum.



Electron Probability

• Since it is impossible to measure the exact position of an electron, we can only calculate the probability of finding an electron at various locations.

• Erwin Schrödinger developed a mathematical model of the electron using a wave function to describe it.– The wave function is used to calculate the probability

of finding electrons at various distances from the nucleus.



Electron Cloud

• The most likely position of the electron in the ground state, according to the wave function, is the same as the Bohr radius.– However, the electron may be

closer or farther away as shown by other probabilities.

• An electron cloud is a picture of the probabilities, where denser means more probable.




Visual Concept

Heisenberg Uncertainty Principle




• The photoelectric effect shows that electromagnetic waves can act like particles. Does it seem possible that particles such as bullets or electrons can show wavelike behavior?– If hundreds of baseballs pass through a doorway, will

they spread out like a sound wave?– Will a beam of electrons going through a small

opening diffract?– After splitting a beam of electrons, could an electron

from one beam interfere constructively with one from the other beam?

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