DEVIL PHYSICSTHE BADDEST CLASS ON

CAMPUSIB PHYSICS

TSOKOS LESSON 6-5:QUANTUM THEORY AND THE UNCERTAINTY PRINCIPLE

Introductory VideoQuantum Mechanics

IB Assessment Statements

Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States

13.1.8. Outline a laboratory procedure for producing and observing atomic spectra.

13.1.9. Explain how atomic spectra provide evidence for the quantization of energy in atoms.

13.1.10. Calculate wavelengths of spectral lines from energy level differences and vice versa.

IB Assessment Statements

Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States

13.1.11. Explain the origin of atomic energy levels in terms of the “electron in a box” model.

13.1.12. Outline the Schrödinger model of the hydrogen atom.

13.1.13. Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy.

Objectives

Describe emission and absorption spectra and understand their significance for atomic structure

Explain the origin of atomic energy levels in terms of the ‘electron in a box’ model

Describe the hydrogen atom according to Schrödinger

Do calculations involving wavelengths of spectral lines and energy level differences

Objectives

Outline the Heisenberg Uncertainty Principle in terms of position-momentum and time-energy

Atomic Spectra

The spectrum of light emitted by a material is called the emission spectrum.

Atomic Spectra

When hydrogen gas is heated to a high temperature, it gives off light

When it is analyzed through a spectrometer, the light is split into its component wavelengths

Atomic Spectra• Different

gases will have emission lines at different wavelengths• Wavelength

s emitted are unique to each gas

Atomic SpectraMercury

• This is called the emission spectrum of the gas• By identifying the

wavelengths of light emitted, we can identify the material

Atomic SpectraHelium

• A similar phenomenon occurs when we pass white light through a gas• On a spectrometer,

white light would show a continuous band of all colors

Atomic SpectraArgon

• When passed through a gas, dark bands appear at the same frequencies as on the emission spectrum• This is called the

absorption spectrum of the gas

Atomic Spectra - Absorbtion

Atomic SpectraNeon

• By trial and error, Johann Balmer found that wavelengths in hydrogen followed the formula,

,...5,4,3

1411

2

nn

R

• But nobody could figure out why• But it did show

the frequencies were not random

Atomic Spectra

Conservation of energy tells us that the emitted energy will be equal to the difference in atomic energy before and after the emission

Since the emitted light consists of photons of a specific wavelength, the energy will be discrete values following the formula,

hchfE

Electron In A Box

de Broglie Wavelength

Electron In A Box

Amplitude is zero at ends of the box Since electron can’t lose energy, the

wave in the box is a standing wave with fixed nodes at x = 0 and x = L

nL2

Electron In A Box

Lhnp

hp

nL

2

2

Electron In A Box

2

22

2

8

2

2

mLhnE

mpE

Lhnp

k

k

•The result is that electron energy is always a multiple of a discrete or quantized value•The same principle applies for electrons surrounding a nucleus

Schrödinger Theory

Wave Function, Ψ(x,t)

Schrodinger equation for hydrogen

Separate equations for electrons in every type of atom

Result is that the energy of an electron in a specific atom is quantized

Schrödinger Theory

Schrodinger’s Theory applied to the electron in a box model yields the following data for a hydrogen atom

Energy is discrete or quantized to one of the energy levels given by n = 1, 2, 3

eVn

E

hkmeC

nCE

2

2

242

2

6.13

2

Schrödinger Theory

Energy levels of emitted photons correspond to energy level changes of electrons

Each time an electron drops in energy level, a photon is released with that energy

Schrödinger Theory

Since E = hf, the photon will have a discrete frequency according to its energy

Knowing the energy level change of the electron, we can compute the frequency and vice versa

Schrödinger TheoryMax Born Interpretation | Ψ(x,t)|2 will give the probability

that an electron will be near position x at time t

Schrödinger Theory Schrodinger’s Theory also predicts the

probability that a transition will occur (| Ψ(x,t)|2)

Explains why some spectral lines are brighter

Heisenberg Uncertainty Principle Applied to position

and momentum: Basis is the wave-

particle duality Can’t clearly explain

behavior based on wave theory or classical mechanics

Heisenberg Uncertainty Principle It is not possible to

simultaneously determine the position and momentum of something with indefinite precision

4hpx

Heisenberg Uncertainty Principle

Making momentum accurate makes position inaccurate and vice versa As Δp approaches 0, Δx

approaches infinity As Δx approaches 0, Δp

approaches infinity

4hpx

Heisenberg Uncertainty Principle Think of aiming a

beam of electrons through a thin slit

Like polarization, we limit wave passage through the slit to a vertical plane

However, the wave will diffract which changes the horizontal position

Heisenberg Uncertainty Principle Even though vertical

position is fairly certain, change in horizontal position means a change in momentum because of the change in the horizontal component of the velocity

Heisenberg Uncertainty Principle Applied to energy and

time: The same principle

can be applied to energy versus time

4htE

Putting It All Together

Unique emission and absorption spectra show that electrons exist at discrete energy levels

The frequency/wavelength of emitted / absorbed light is a function of the electron’s energy level

Since each element has unique electron energy levels, the light it emits/absorbs is unique to that element

Putting It All Together

Schrödinger developed a wave function, Ψ(x,t), to describe electron position vs. time in hydrogen

Wave functions different for each element

Born gave us the probability of finding an electron at a given point at a given time as |Ψ(x,t)|2

Putting It All Together

But Heisenberg showed that trying to find the electron is difficult

4hpx

4htE

Σary Review

Can you describe emission and absorption spectra and understand their significance for atomic structure?

Can you explain the origin of atomic energy levels in terms of the ‘electron in a box’ model?

Can you describe the hydrogen atom according to Schrödinger?

Σary Review

Can you do calculations involving wavelengths of spectral lines and energy level differences?

Can you outline the Heisenberg Uncertainty Principle in terms of position-momentum and time-energy?

IB Assessment Statements

Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States

13.1.8. Outline a laboratory procedure for producing and observing atomic spectra.

13.1.9. Explain how atomic spectra provide evidence for the quantization of energy in atoms.

13.1.10. Calculate wavelengths of spectral lines from energy level differences and vice versa.

IB Assessment Statements

Topic 13.1, Quantum Physics: Atomic Spectra and Atomic Energy States

13.1.11. Explain the origin of atomic energy levels in terms of the “electron in a box” model.

13.1.12. Outline the Schrödinger model of the hydrogen atom.

13.1.13. Outline the Heisenberg uncertainty principle with regard to position-momentum and time-energy.

QUESTIONS?

Homework

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