Download Chapter 28 Atoms

Chapter 28
Atoms
Alexandra Reed
Rebecca Ray
Chelsea Mitchell
Lena Kral
Niels Bohr
- history -
Neils Bohr



full name: Niels Henrick David Bohr
born on October 7, 1885.
Bohr attended the local University of
Copenhagen partly because his
father was a professor of physiology
there and mostly because his
childhood was filled with the
presence of scientists.
Niels Bohr




Master’s degree in 1909
doctorate in 1911
After graduation he moved to
Cambridge to study with J. J.
Thomson. They didn’t agree.
After a meeting with Earnest
Rutherford, he decided to move
with him to Manchester in 1912.
Niels Bohr

Bohr felt it greatly extended the
understanding of nuclear fission. He
thought, the development of the fission
bomb was a great achievement.
However with every great scientific
discovery there were limits that need to
be set upon it. He was deeply concerned
about the control of these highly
powerful weapons and urge for the need
of international cooperation.
Chapter 28.1




The energy of an orbiting electron in an atom is
the sum of the kinetic energy of the electron and
the potential energy resulting from the attractive
force between the electron and the nucleus.
The energy of an electron in an orbit near the
nucleus is less than that of an electron in an orbit
farther away because work must be done to move
an electron to orbits farther away from the
nucleus.
The electrons in excited states have larger orbits
and correspondingly higher energies.
Bohr postulated that the change in the energy of
an atomic electron when a photon is absorbed is
equal to the energy of the photon. That is:
ΔE = hf = Eexcited – Eground
Predictions



of the Bohr Model
Bohr’s calculations start with Newton’s law,
F=ma, applied to an electron of mass m and
charge –q, in a circular orbit of radius r about a
massive particle, a proton, of charge q.
Fc = mac
Kq2/r2 = mv2/r
K= constant (9x109 Nm2/C2)
q= charge
r= radius
m= mass
v= centripetal velocity
Bohr Model
Formulas
The angular momentum can only have certain values, given by the
equation:
mvr = nh/2 π
h = Planck’s constant (6.63x10-34 m2kg/s)
n = integer
*Because the quantity can only be integer values, it is said to be
quantized.
-Combining Newton’s Law with the quantization of angular momentum
gives the predicted radius:
rn = (h2n2)/(4 π 2Kmq2)
*When you substitute in numerical values for the constants, you get:
rn= (5.3x10-11m)n2
-The total energy of the electron in its orbit is given by the equation:
En = (-2 π 2K2mq4)/(h2n2)
*When you substitute in numerical values for the constants, you get:
En = -13.6 eV/n2 = -2.17x10-18J/n2
Example Problems
For the hydrogen atom, determine a. the energy of
the innermost energy level (n = 1), b. the energy
of the second level, and c. the energy difference
between the first and second energy levels.
a. E1 = -13.6eV / (1)2 = -13.6 eV
b. E2 = -13.6eV / (2)2 = -3.4 eV
c. ΔE = Ef – Ei = E2 – E1 = -3.4 eV – (-13.6 eV) =
10.2 eV
More Example Problems!
An electron in an excited hydrogen atom drops from the
second energy level to the first energy level. A. Determine
the energy of the photon emitted. B. Calculate the frequency
of the photon emitted. C. Calculate the wavelength of the
photon emitted
A. hf = Ei – Ef = E2 – E1
=-3.4 eV – (-13.6 eV) = 10.2 eV
B. f = E/h
=((10.2 eV)(1.6x10-19 J/eV)) / (6.63x10-34 J/Hz) = 2.46x1015 Hz
C. λ= c/f = (3x108 m/s )/(2.46x1015 Hz) = 1.22x10-7m
Even More Example Problems ;)
Calculate the radius of the orbital associated with
the energy levels E3 of the hydrogen atom.
E3 = -13.6eV/(3)2 = -1.51eV
r3 =(h2n2)/(4π2Kmq2)
= (5.3x10-11m)n2
= (5.3x10-11m)(3)2
=4.77x10-10
Wake Up!!
Background Info Section 28.2


In 1926, the German physicist Erwin
Schroedinger used de Brogli’s wave model to
create a quantum theory of atom based on
waves. The theory does not provide a simple
planetary picture of an atom as in the Bohr
model. In particular, the radius of the electron
orbit is not like the radius of the orbit of a planet
about the sun.
In wave particle nature matter means that it is
impossible to know both the position and
momentum of an electron at the same time. Thus
the modern Quantum Model of the atom
predicts only the probability that an electron is at
a specific location.
Background Info Cont.


The most probable distance of the
electron from the nucleus in hydrogen is
found to be the same as the radius of the
Bohr orbit.
The probability that the electron is at any
radius can be calculated, and a threedimensional plot can be constructed that
shows regions of equal probability. The
region in which there is a high probability
of finding the electron is called the
Electron Cloud.
Background Info Cont. Again!!!

Even though the quantum model of the
atoms is difficult to visualize, quantum
mechanics, which uses the Bohr model,
has been extremely successful in
predicting many details of the structure of
the atom. These details are very difficult
to calculate exactly for all but the
simplest atom. Guided by quantum
mechanics, chemists have been able to
create new and useful molecules not
otherwise available.
Lasers






Light
Amplification by
Stimulated
Emission of
Radiation
Lasers produce light that is directional,
powerful, monochromatic, and coherent.
Uses for Lasers





Medical
Eye Surgery
Plastic Surgery
Cut Steel
Destroying the World
Formula for Section 28.2
The Bohr quantization condition:
nλ = 2 π r
n = whole number multiple of λ
λ = wavelength of the electron
r = radius
Example Problem
If the wavelength of an electron is
450 nm, and there are 2 electrons,
what is the radius of the electron?
nλ = 2 π r
(2)(450 nm) = (2)(π)(r)
2π
2π
143.24 nm = r
Every Day needs an Explosion!!
http://www.youtube.co
m/watch?v=bw85r24W
W3s