Lecture 5: the Hydrogen Atom

Transcription

1 Lecture 5: the Hydrogen Atom 1. Hydrogen atom: energy levels in the Bohr model 2. Emission lines: atoms releasing energy as electrons fall from level to level 3. Absorption lines: electrons being bumped from one level to a higher one

2 Particles and waves: everything is both 1. Light is a wave, but it interacts with matter as a particle: this is a consequence of quantum mechanics 2. What does this mean in practice? a. intensity of electric field reflects probability to interact + b. if an interaction occurs, it produces a discrete interaction 3. A little packet of energy is given to the electron: the quantum in quantum mechanics 6. If you don t like this, too bad, get used to it: all matter is like this! electrons and protons, which you normally think of as particles, are waves as well!

3 Photo-electric effect 1. Einstein in 1905 proposed the photon to explain the photoelectric effect: light can kick electrons out of a metal plate (rest of the apparatus is to measure the rate of kicking through current flow) 2. Low frequency light NEVER releases electrons no matter how bright the light is 3. High enough frequency light kicks out electrons --- the number of electrons depends on the brightness of the light: the frequency of light is related to the energy in each photon, the brightness of light is related to how many photons there are

4 Bohr model of hydrogen Hydrogen (H) is what the Sun is made of, mostly, and is the most common element in the Universe, accounting for > 70% of ordinary matter. So we had better understand it pretty well. Luckily, that is possible (though not exactly simple).

5 Bohr model of hydrogen

6 Bohr model of hydrogen electron + proton velocity + force

7 Bohr model of hydrogen velocity + force an incoming photon can increase the orbital energy of the electron and bump it from a low state to a high state

8 Bohr model of hydrogen velocity + force

9 Bohr model of hydrogen +

10 Bohr model of hydrogen +

11 Bohr model of hydrogen +

12 Bohr model of hydrogen +

13 Bohr model of hydrogen the energy differences between various states of hydrogen are therefore of great importance -- photons of frequencies/wavelengths that match these energy differences are very easily absorbed e.g., the Lyman series: Ly-alpha is at 1216 Angstroms

14 Bohr model of hydrogen the energy differences between various states of hydrogen are therefore of great importance -- photons of frequencies/wavelengths that match these energy differences are very easily absorbed or the Balmer series: H-alpha is at 6563 Angstroms

15 Bohr model of hydrogen of course photons that are energetic enough, can eject the electron from the atom completely, in a process called ionization ionizing photons: < 912 Angstroms

16 Absorption lines if a hydrogen atom is sitting in the ground state, it can absorb photons very easily, but only if they exactly the right energy to put it into a higher state.

17 Absorption lines if a hydrogen atom is sitting in the ground state, it can absorb photons very easily, but only if they exactly the right energy to put it into a higher state.

18 Absorption lines if a hydrogen atom is sitting in the ground state, it can absorb photons very easily, but only if they exactly the right energy to put it into a higher state.

19 Absorption lines if a hydrogen atom is sitting in the ground state, it can absorb photons very easily, but only if they exactly the right energy to put it into a higher state.

20 Example: absorption in the atmosphere of the Sun causes emergent spectrum to differ f from a black-body spectrum

21 Fraunhofer lines -- from H plus other elements and molecules in Sun s atmosphere

22 Emission lines if a hydrogen atom is sitting in an excited state, it can fall down a level (or more) --- the energy has to go somewhere, and it goes out as a photon!

23 Emission lines if a hydrogen atom is sitting in an excited state, it can fall down a level (or more) --- the energy has to go somewhere, and it goes out as a photon! this particular case, falling from level 3 to level 2, is an important transition known as H-alpha or Balmer-alpha, since it is the lowest rung of the Balmer series

24 Again, a good example from the Sun: (as seen at wavelength of H-alpha) light in flares are easily seen at this wavelength because they are filled with H atoms with electrons falling from 3 to 2

25 How do astronomers measure spectra? one way is to make a glass filter that is only transparent to a certain range of wavelengths --- but then you can only observe one range of wavelengths at a time

26 Prisms and diffraction gratings: allow you to break up the light by wavelength and observe entire spectrum simultaneously This measurement of the Sun s spectrum is the result of using a diffraction grating