Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far:...
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Transcript of Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far:...
![Page 1: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/1.jpg)
Quantum Mechanics
Through the Looking Glass
![Page 2: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/2.jpg)
This is how the model of the atom has developed so far:
Rutherford
ThomsonDemocritus Dalton
![Page 3: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/3.jpg)
c = where c =3.00 x 108 m/s
![Page 4: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/4.jpg)
Sample Problem: The yellow light given off by a sodium lamp has a wavelength of 589 nm. What is the frequency of this radiation?
c = , where c =3.00 x 108 m/s
3.00 x 108 m/s = 589 nm 1 m
1x109nm
= 5.08 x 1014 s 1-
![Page 5: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/5.jpg)
Planck’s Theory: Energy is released incrementally as
individual packets of energy called quanta, where the change in energy of a system is E = h,
2h,…n h and h(plank’s constant) =
h = 6.63 x 10-34 J-s
![Page 6: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/6.jpg)
we know from the previous problem: c = , that = 5.08 x 1014 s 1-
since E = h and h (plank’s constant) = 6.63 x 10-34 J-s
E = (6.63 x 10-34 J-s )(5.08 x 1014 s 1- )
E = 3.37 x 10-19 J
Sample Problem: Calculate the smallest increment of energy that an object can absorb from yellow light
whose wavelength is 589 nm
![Page 7: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/7.jpg)
A Continuous Spectrum
![Page 8: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/8.jpg)
Light is a form of ...
Electromagnetic Radiation
![Page 9: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/9.jpg)
An Emission Spectrum...…is produced when a gas is placed under reduced pressure...
...as a high voltage is applied
![Page 10: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/10.jpg)
Balmer’s Description of the Emission Spectrum of Hydrogen
= C 1
22
- 1
n2
where n = 3, 4, 5, 6… and C = 3.29 x 1015 s-1
![Page 11: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/11.jpg)
Bohr’s Model of the Atom (1914)
Limited the path of electrons to circular orbits with discrete energy (quantum energy levels)
Explained the emission spectrum of hydrogen
![Page 12: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/12.jpg)
0 Ao
2.12 Ao
4.77 Ao
n = 1
n = 2
n = 3
-2.18 x 10 -18 J
0
-0.545 x 10 -18 J
-0.242 x 10 -18 J
Radii and Energies of the Three Lowest Energy orbits in the Bohr Model
radius = n2 (5.3 x 10-11m)
0.53 A
En = -RH1n2 where RH = 2.18 x 10 -18J
En = -RH
1
2=
![Page 13: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/13.jpg)
Hydrogen’s Spectrum is Produced When
Electrons are excitedfrom their ground state
Electrons appear in excited state
electrons transfer from an excited state
photons produced
Electrons return totheir ground state
energy is absorbed
![Page 14: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/14.jpg)
Lyman Series
Balmer Series
Paschen Series
•Ultraviolet
•Visible and Ultraviolet
•Infrared
![Page 15: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/15.jpg)
Explaining the Emission Spectrum of Hydrogen
since E = E f - E i
then E = -RH
1nf
2-
1ni
2
![Page 16: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/16.jpg)
Sample Problem: Calculate the wavelength of light that corresponds to thetransition of the electron from the n = 4 to the n=2 state of the hydrogen atom.
RH1
ni2
-1
nf2
E =
2.18 x 10-18J1
42-
1
22E =
-4.09 x 10-19 JE =
= E h
= -4.09 x 10-19 J
6.63 x 10-34 J-s
= 6.17 x 1014 s -1
= c
= 3.00 x 108 m/s
6.17 x 1014 s -1
= 4.86 x 10-7 m = 486 nm (green)
![Page 17: Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Rutherford Thomson Democritus Dalton.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5514dc3655034640138b65f7/html5/thumbnails/17.jpg)