Physics and the Quantum Mechanical Model

1. Physics and the Quantum Mechanical Model

2. Connection • The Quantum Mechanical Model grew out of the study of light. • Scientists originally believed light was a particle, just like matter. • However, by 1900, it was generally accepted that light was a wave phenomenon. • Light consisted of electromagnetic waves

3. Light • Electromagnetic Radiation includes radio waves, microwaves, infrared waves, visible light, ultraviolet waves, x-rays, and gamma rays • All light travels at 2.998 x 108 m/s, in a vacuum (absence of matter)

4. Waves • Electromagnetic waves (light) have the same structure as your normal wave. • Wavelength () is the distance between two consecutive crests (or troughs) (unit => m or nm) • Amplitude (A) is the height of a wave, or the distance from the origin to the crest. (unit => m or nm) • Frequency () is the number of wave cycles to pass a given point per unit of time (unit => Hz or 1/s)

5. Equation • Wavelength and Frequency have an inverse relationship. • They are related by the velocity or speed of light (c) – see above • The equation that relates frequency, wavelength, and speed of light is: • c = .

6. Spectra • A spectrum is the range of wavelengths associated with light. • The electromagnetic spectrum gives the range of wavelengths of all types of light. • Visible white light produces the continuous spectrum that we associate with the colors of the rainbow (ROY G BIV) • However, not all light produces a continuous spectrum. • When matter becomes electrically charged, it can begin to give off light. • The light given off by an element is called an Atomic Emission Spectrum. • This spectrum is discontinuous. • It appears as a series of disconnected lines on the electromagnetic spectrum.

7. Uses of Spectra • Scientists use an Emission Spectrograph to analyze the wavelengths of light given off by charged elements. • The emission spectrograph gives the entire range of wavelengths associated with the light from the element. • Scientists have found that no two elements share the exact same Atomic Emission Spectrum. • The AES can be used like a fingerprint to determine the types of element in a sample of matter • Very useful in astronomy • A spectroscope can be used to analyze the spectrum found within the visible light range.

8. Quantum Concept and Photoelectric Effect • What we knew about energy said the spectra of elements should be continuous because… • There should be no limit to how small the Energy lost or gained by an object can be. • Max Planck attempted to explain the discrepancy • Examined the color change of Iron as it is heated. • Explanation: Energy of a body changes in small discrete units

9. E = h. • So…The amount of radiant Energy (light) absorbed or emitted is proportional to the frequency of the radiation • E  or E = h. • Planck calculated the value of the proportionality constant • Planck’s constant: h = 6.6262 x 10-34J.s

10. E = h. • This equation allowed scientists to determine the value of a quantum. • Because…when an electron moves from a higher energy level to a lower energy level, it will emit energy in the form of light. We can determine the wavelength and frequency of the light emitted and use it to calculate the energy associated with these electron transitions.

11. E = h. • The energy calculated using Planck’s equation equals the energy of a quantum. • So… • Low-frequency radiation --- Small Energy change • High-frequency radiation --- Large Energy change

12. Einstein • Einstein proposed that light could be described as quanta of energy that behaved like particles • Called them Photons • Energy of a Photon => E= h. • This Dual Wave-Particle Behavior of light explains the Photoelectric Effect.

13. Photoelectric Effect • Metals eject electrons called photoelectrons when light shines on them. • Alkali metals are the most susceptible. • Not all wavelengths of light create this phenomenon • The wavelength must have a threshold value of energy (Ladder analogy) • In monochromatic light, all photons have the same Energy • Solar cells use the photoelectric effect to produce electricity.

14. Wavelength of a Particle • Louis de Broglie wondered if particles of matter could behave like waves • If light could do both, why not matter… • He developed an equation that predicted the wavelength of a moving particle of matter = __h__ m . v •  = wavelength of a moving particle of matter • h = Planck’s constant • m = mass of particle • v = velocity of particle

15. Classical Mechanics vs. Quantum Mechanics • Quantum Theory created a split in the area of mechanics. The quantum concept did not fit with the traditional ideas about how matter and energy behaved. Classical Mechanics • describes the motion of large bodies • Therefore, it appears that the body can gain or lose energy in any amount

16. Quantum Mechanics • Describes the motion of subatomic particles and atoms as waves • Therefore, they gain or lose energy in packages called quanta • Includes the uncertainty principle • Because these particles are extremely small, they are affected by interactions with photons. • Heisenberg’s uncertainty principle states that It is impossible to know both the position and the velocity of a particle at the same time. • Only way to know precise position of a subatomic particle is for a photon (light) to collide with it. • The collision will change the velocity of the particle • Therefore, we can’t know both at the exact same time.