The Bohr Model Put the four equations from the previous slide together to show that h’e, Tme? r =n 1 me E, n2 8eh? In general, a negative sign indicates a bound state. The system must receive energy in order to be broken up. Here, breaking up the system means removing the electron (ionizing the atom). 13.6eV 々? Planck's constant h = 6.626x10-4 Js Electric permittivity of the vacuum E, = 8.854 x10-12, Nm? m =9.11x10" kg Mass of the electron -31 Charge of the electron e =1.602 x10-1ºC

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Chapter1: Units, Trigonometry. And Vectors
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Combine the equations on slide 10 to obtain the expressions for the radius of the electron orbit and the energy of the hydrogen atom given on slide 11.

The Bohr Model
Put the four equations from the previous slide together to show that
h'e,
Ame?
In general, a negative sign indicates a bound state. The
system must receive energy in order to be broken up.
Here, breaking up the system means removing the
electron (ionizing the atom).
1 me
13.6 eV
En
n?
8egh?
n°
Planck's constant
h = 6.626x1034 Js
E, = 8.854 x 10-12
Nm?
Electric permittivity of
the vacuum
m = 9.11x1031
kg
Mass of the electron
Charge of the electron
e =1.602 x10-1ºC
leV =1.602 x10-1º J
Transcribed Image Text:The Bohr Model Put the four equations from the previous slide together to show that h'e, Ame? In general, a negative sign indicates a bound state. The system must receive energy in order to be broken up. Here, breaking up the system means removing the electron (ionizing the atom). 1 me 13.6 eV En n? 8egh? n° Planck's constant h = 6.626x1034 Js E, = 8.854 x 10-12 Nm? Electric permittivity of the vacuum m = 9.11x1031 kg Mass of the electron Charge of the electron e =1.602 x10-1ºC leV =1.602 x10-1º J
The Bohr Model
The circumference of the electron trajectory
2πr,- ηλ
must correspond to an integer number of
wavelengths.
A = wavelength of the wave matter associated
with the electron.
h
The deBroglie Hypothesis (the relationship
between the momentum of the electron and its
(b)
mv,
wave matter wavelength).
m = mass of the electron
v, = speed of the electron on orbit n (of radius r)
e(-e)
Total energy of the atom when the electron is on
orbit n = kinetic energy of the electron + potential
energy of the proton-electron system.
1
E, -m² +
Electron, -e
F
Recall U =
from earlier in the semester
4TE,r
Proton, +e
my?
e?
The Coulomb force is the centripetal force.
Recall F
Coulomb
from earlier in the semester
4TE,r2
my?
Recall F
from Physics 1
centripetal
Transcribed Image Text:The Bohr Model The circumference of the electron trajectory 2πr,- ηλ must correspond to an integer number of wavelengths. A = wavelength of the wave matter associated with the electron. h The deBroglie Hypothesis (the relationship between the momentum of the electron and its (b) mv, wave matter wavelength). m = mass of the electron v, = speed of the electron on orbit n (of radius r) e(-e) Total energy of the atom when the electron is on orbit n = kinetic energy of the electron + potential energy of the proton-electron system. 1 E, -m² + Electron, -e F Recall U = from earlier in the semester 4TE,r Proton, +e my? e? The Coulomb force is the centripetal force. Recall F Coulomb from earlier in the semester 4TE,r2 my? Recall F from Physics 1 centripetal
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