13.1 The Wave Nature of Matter - seriouslysilly - homeWav… · · 2015-03-1113.1 Wave Nature &...
13
13.1 Wave Nature & Atomic Spectra.notebook 1 March 11, 2015 13.1 The Wave Nature of Matter
Transcript of 13.1 The Wave Nature of Matter - seriouslysilly - homeWav… · · 2015-03-1113.1 Wave Nature &...
13.1 Wave Nature & Atomic Spectra.notebook
1
March 11, 2015
13.1 The Wave Nature of Matter
13.1 Wave Nature & Atomic Spectra.notebook
2
March 11, 2015
WaveParticle Duality
13.1 The Wave Nature of Matter
13.1 Wave Nature & Atomic Spectra.notebook
3
March 11, 2015
WaveParticle DualityThe photoelectric effect demonstrates light particle like nature, although we have studied the wave nature of light prior to this. Since electromagntic radition propgates like a wave but exchanges energy like a particle, we say it has a waveparticle duality.
In 1923 Louis de Broglie theorized that if waves can act like particle, particles should be able to act like waves. He suggested that a particle of mass m and speed v, should have a momentum that is associated with its wavelength:
λ= h/p where p = mv this is called its de Broglie wavelength.
Large particles have very small wavelengths so they do not display wavelike behaviour:
A baseball of mass 0.15 kg having a speed 40 m/s
λ= h/p = 6.63 x 1034Js/(0.15kg)(40 m/s) = 1.1 x 1034m
It has been shown that tiny particles, like electrons, demonstrate wave characteristics, like diffraction and interference patterns.
Louis de Broglie
13.1 The Wave Nature of Matter
13.1 Wave Nature & Atomic Spectra.notebook
4
March 11, 2015
Electrons in a difraction experiement are accelerated through a potential difference of 200V. What is the de Broglie wavelength of these electrons?
13.1 The Wave Nature of Matter
13.1 Wave Nature & Atomic Spectra.notebook
5
March 11, 2015
Davisson and Germer experiment
• In this experiment, electrons of kinec energy 54eV were directed at a surface of nickel where a single crystal had been grown and were scaered by it.
• Using the Bragg formula (When x‐rays are scaered from a crystal lace, peaks of scaered intensity are observed) and the known separaon of the crystal atoms allowed the determinaon of the wavelength which has then seen to agree with the De Broglie formula.
At certain angles the intensity detected followed that of superimposed waves.
13.1 The Wave Nature of Matter
13.1 Wave Nature & Atomic Spectra.notebook
6
March 11, 2015
13.1 The Wave Nature of Matter
Page 235 Hamper
#9. An electron is accelerated by a p.d. of 100V. Calculate its
a) KE in eVb) KE in joulesc) de Broglie wavelength
#10. Calculate the de Broglie wavelength for a car of mass 1000 kg travelling at 15 ms1. Why won't you ever see a car diffract?
13.1 Wave Nature & Atomic Spectra.notebook
7
March 11, 2015
13.1 Atomic Spectra & Atomic Energy States
13.1 Wave Nature & Atomic Spectra.notebook
8
March 11, 2015
Niels Bohr & Atomic Spectra
Soilds emit very distinctive bands of color if they are incandesent and viewed through a spectroscope an emission spectrum.
Niels Bohr suggested this was due to the excitation of electrons to jump from one electron energy level (specific orbit) to another and then fall back down, emitting a photon of specific wavelength.
Specfic packets of energy (quanta) is needed for this to happen to electrons.
The Balmer Series describes mathematically the component wavelengths of the hydrogen spectra:
Niels found that the excited state was a fraction of the energy of the ground state:
R = 1.097 x 107 m1
then
if &
or
This formula represnts the energy to remove an electron from ground state to infinity ground state energy works out to E1 = 13.6 eV, the ionization energy for hydrogen.
For Helium (atomic number Z = 2) the inozation energy is given by:
13.1 Atomic Spectra & Atomic Energy States
13.1 Wave Nature & Atomic Spectra.notebook
9
March 11, 2015
Each possible drop between atomic energy levels in an atom corresponds to the emission of one specific frequency of photon.
This results in one line in an element’s emission spectrum. Three lines in hydrogen’s spectrum are shown here, along with the energy jumps that they correspond to.
13.1 Atomic Spectra & Atomic Energy States
13.1 Wave Nature & Atomic Spectra.notebook
10
March 11, 2015
13.1 Atomic Spectra & Atomic Energy States
Just as an electron can drop between energy levels in an atom, releasing a single photon, it can also jump up one or more energy levels if it absorbs a photon of the right energy.
One result of this is that shining a continuous spectrum of light at a transparent material leads to a few discrete frequencies being absorbed, while the rest are transmitted. This forms an absorption spectrum.
13.1 Wave Nature & Atomic Spectra.notebook
11
March 11, 2015
Since then the wavelength og the photon is:
When an excited electron drops from energy level n = j to a lower on n = i a photon of energy is emitted, the energy of the photon is the difference between the two energy levels:
Example:The first five energy levels of an atom are given as:
3eV n = 54eV n = 4
7eV n = 3
15eV n = 2
62eV n = 1
a) If the atom begins in the n = 3 level, what photon energies could be emitted as it returns to the ground state?
b) What could happen if this atom, while in an undetermined energy state, were bombarded with a photon of energy 10 eV?
13.1 Atomic Spectra & Atomic Energy States
13.1 Wave Nature & Atomic Spectra.notebook
12
March 11, 2015
a) If the atom begins in the n = 3 level, what photon energies could be emitted as it returns to the ground state?
In n= 3 the atom could return to ground state via 3 1, or from 3 2 and then 2 1.
E31 = E3 E1 = (7eV)(62eV) = 55eV
E32 = E3 E2 = (7eV)(15eV) = 8eVE21 = E2 E1 = (15eV)(62eV) = 47eV8ev+47eV = 55eV
b) What could happen if this atom, while in an undetermined energy state, were bombarded with a photon of energy 10 eV?
Since no two energy states in this atom are separated by 10eV, the atom could not absorb a 10eV photon, so nothing would happen.
Example:The first five energy levels of an atom are given as:
3eV n = 54eV n = 4
7eV n = 3
15eV n = 2
62eV n = 1
13.1 Atomic Spectra & Atomic Energy States
13.1 Wave Nature & Atomic Spectra.notebook
13
March 11, 2015
13.1 Atomic Spectra & Atomic Energy States
Hamper HL page 232 Q’s 5‐8.
