1. Chapter 27 Quantum Theory

2. Objectives
27.1 Describe the spectrum emitted by a hot body and explain the basic theory that underlies the emission of hot-body radiation
27.1 Explain the photoelectric effect and recognize that quantum theory can explain it, whereas the wave theory cannot
27.1 Explain the Compton effect and describe it in terms of the momentum and energy of the photon

3. Objectives
27.1 Describe the experiments that demonstrate the particle like properties of electromagnetic radiation
27.2 Describe evidence of the wave nature of matter and solve problems relating wavelength to particle momentum
27.2 Recognize the dual nature of both waves and particles and the importance of the Heisenberg uncertainty principle

4. Black Body Radiation The hotter an object is
The more energy radiated away
The higher peak frequency emitted by the object
Every object emits electromagnetic waves
Result of vibrating particles and electrons falling down

7. Quantized Energy
The energy an atom has is quantized, meaning it can only have certain energies
Atoms in a solid can only vibrate at certain/specific frequencies
Energy is emitted when the atom changes its vibration
E = nhf
Where n is an integer, h is Planck’s constant, and f is frequency. 6.63x 10-34
Energy = 2hf, or 3hf, or 4hf and so on

8. Quantized Energy
If an atom of energy 4hf were to change its energy to 3hf, it would emit radiation, equal to 1hf.
5hf to 3hf would emit 2hf amount of energy
Going up requires receiving certain energies as well
These distinct packets of energy we call photons

9. Photoelectric Effect
The emission of electrons when EM radiation hits an object is known as the photoelectric effect

10. Photoelectric Effect
Not all radiation results in electrons given off. Need a minimum frequency, called the threshold frequency

11. Photoelectric Effect
Different materials have different threshold frequencies due to their differences in structure
Chem Connection
Ionization Energy
Electron Orbitals
Metals low
Non-metals high

12. Photoelectric Effect
If a red EM wave doesn’t ionize an object, 2red, 3red, or 1000red won’t either.
A bulb that produces more light doesn’t make it ionize
Need the right frequency

14. Common Uses of Photoelectric Effect
Garage door openers
Doors that open automatically for you when you get close

15. Photoelectric Effect
Threshold Frequency is the minimum amount of energy needed
What happens to the extra energy?
Turns into Kinetic Energy of the electron
KE = hf – hf0
Kinetic Energy of electron equals the incident frequency minus the threshold frequency
Electrons can’t store energy, only get one photon (again, 2reds doesn’t help)

16. Photoelectric Effect
Not every electron in an atom requires the same amount of energy to escape.
Different subshells
They will leave with different amounts of KE

17. Electron Volt
Since electrons are small, and a joule is a very large unit, there is another way to discuss energy of an electron
The electron volt (eV)
1 eV = 1.6 x Joules
Same as electron charge for convience
This is how much energy an electron gets when it is accelerated across a 1.0 volt potential different

18. Electron Volt

19. Energy of an EM wave revisited
E = nhf rearranged for electron volts
E = (1240 eV * nm) / wavelength
How much energy (in eV) does a photon of wavelength 620 nm have?

20. Stopping Potential How we determined the KE of electrons
Adjust Voltage until the electrons don’t make it

21. Simulator

22. Work Function
The threshold frequency is related to the energy needed to free the most weakly bound electron from a an object. This is called the work function
To find this energy, use
E = (1240 eV/nm) / wavelength

23. Questions
1) The stopping potential for a photoelectric cell is 5.7 V. Calculate the KE of the emitted photoelectrons in eV.
The threshold wavelength of zinc is 310 nm
A) Find the threshold frequency of zinc
B) What is the work function in eV of zinc?
C) Zinc is illuminated by UV of 240 nm. What is the KE of the electron emitted?

24. Answered 1) 5.7 eV is the KE of the emitted electrons
A) c / wavelength = frequency
Frequency = 9.7 x 1014
B) / 310 = 4.0 eV
C) (1240 / 240) – (1240 / 310) = 1.2 eV

25. Compton Effect
Even though photon’s do NOT have mass*, they still have momentum
*Energy can be converted to mass technically
Momentum of a photon is equal to
Planck’s Constant Wavelength

28. What it all means
The initial photon transfers energy and momentum to the electrons. This transfer of momentum leads to a net loss of energy for the ejected photons (they have a longer wavelength)

29. Shifting to waves
The last ideas are evidence that photons are particles. We will now discuss wavelike properties of photons

30. de Broglie Wavelength
Since electrons diffract, de Broglie suggested they were also waves.
Since everything is made of electrons/protons, they should all have wavelike characteristics
Wavelength (de Broglie) = Planck’s Constant / Momentum of object

31. Wavelength of Baseball
Wavelength = 6.63 x / (0.25 kg)(20m/s) = 1.3 x 10-34
Too small to have an observable effect
What about an electron?
Its wave is large enough to be significant compared to itself

32. Question
An electron has a speed of 5.1 million m/s. What is its de Broglie Wavelength?
Momentum = Mass x Velocity
P = (9.11 x kg)(5.1 million m/s)
h / p = wavelength
6.63 x / 4.6 x 10-24
0.14 nm

33. Where are you electron?
How do we see where an electron is (it’s location)?
By having a photon hit it.
But doesn’t the photon move the electron?
Yes, so if we know where it is, we have no idea where it is off too

34. Heisenberg Uncertainty Principle
The more certain you are of location, the less certain you are off the momentum