lecture 32
Download
Skip this Video
Download Presentation
LECTURE # 32

Loading in 2 Seconds...

play fullscreen
1 / 35

LECTURE # 32 - PowerPoint PPT Presentation


  • 130 Views
  • Uploaded on

LECTURE # 32. HYDROGEN ATOM PARTICLE DOUBLE-SLIT PROBABILITY. PHYS 270-SPRING 2010 Dennis Papadopoulos. MAY 3 2010. 1. Bohr’s Model of Atomic Quantization. An atom consists of negative electrons orbiting a very small positive nucleus.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' LECTURE # 32' - kare


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
lecture 32

LECTURE # 32

HYDROGEN ATOM

PARTICLE DOUBLE-SLIT

PROBABILITY

PHYS 270-SPRING 2010

Dennis Papadopoulos

MAY 3 2010

1

bohr s model of atomic quantization
Bohr’s Model of Atomic Quantization
  • An atom consists of negative electrons orbiting a very small positive nucleus.
  • Atoms can exist only in certain stationary states. Each stationary state corresponds to a particular set of electron orbits around the nucleus. These states can be numbered 2, 3, 4, . . . , where n is the quantum number.
  • Each stationary state has an energy En. The stationary states of an atom are numbered in order of increasing energy: E1 < E2 < E3 < …
  • The lowest energy state of the atom E1 is stable and can persist indefinitely. It is called the ground state of the atom. Other stationary states with energies E2, E3, E4,. . . are called excited states of the atom.
bohr s model of atomic quantization1
Bohr’s Model of Atomic Quantization

5. An atom can “jump” from one stationary state to another by emitting or absorbing a photon of frequency

where h is Planck’s constant and and ΔEatom = |Ef – Ei|.

Ef and Eiare the energies of the initial and final states. Such a jump is called a transition or, sometimes, a quantum jump.

bohr atom
Bohr Atom

r=n2aB ,

aB= (h/2p)2/(ke2m)=.0529 nm

En=-E1/n2

E1=13.6 eV

slide5

an integer number of wavelengths fits into the circular orbit

where

Photons

p=hn/c=

h/l

l is the de Broglie wavelength

the bohr hydrogen atom
The Bohr Hydrogen Atom

The radius of the electron’s orbit in Bohr’s hydrogen atom is

where aB is the Bohr radius, defined as

The possible electron speeds and energies are

the hydrogen spectrum
The Hydrogen Spectrum

According to the fifth assumption of Bohr’s model of atomic quantization, the frequency of the photon emitted in an n→ m transition is

The corresponding wavelengths in the hydrogen spectrum are then

slide16

A photon with a wavelength of 414 nm has energy Ephoton = 3.0 eV. Do you expect to see a spectral line with = 414 nm in the emission spectrum of the atom represented by this energy-level diagram? If so, what transition or transitions will emit it?

slide17

A photon with a wavelength of 414 nm has energy Ephoton = 3.0 eV. Do you expect to see a spectral line with λ = 414 nm in the absorption spectrum of the atom represented by this energy-level diagram? If so, what transition or transitions will absorb it?

slide18

A photon with a wavelength of 414 nm has energy Ephoton = 3.0 eV. Do you expect to see a spectral line with = 414 nm in the emission spectrum of the atom represented by this energy-level diagram? If so, what transition or transitions will emit it?

slide19

The Atom According to Bohr,

who was (mostly) right

slide20

We said earlier that Bohr was mostly right…so where did he go wrong?

  • Failed to account for why some spectral lines are stronger than others. (To determine transition probabilities, you need QUANTUM MECHANICS!) Auugh!
  • Treats an electron like a miniature planet…but is an electron a particle…or a wave?
slide31

Energy E intercepted by an area A=Hdx

WAVE PICTURE

PHOTON PICTURE

connecting the wave and photon views
Connecting the Wave and Photon Views

The intensity of the light wave is correlated with the probability of detecting photons. That is, photons are more likely to be detected at those points where the wave intensity is high and less likely to be detected at those points where the wave intensity is low.

The probability of detecting a photon at a particular point is directly proportional to the square of the light-wave amplitude function at that point:

probability density
Probability Density

We can define the probability density P(x) such that

In one dimension, probability density has SI units of m–1. Thus the probability density multiplied by a length yields a dimensionless probability.

NOTE: P(x) itself is not a probability. You must multiply the probability density by a length to find an actual probability.

The photon probability density is directly proportional to the square of the light-wave amplitude:

ad