HOMEWORK – DUE THURSDAY 10/22/15 HW-BW 7.2 (Bookwork) CH 7 #’s 39, 42, 48-52 all, 55-60 all, 64, 69, 71, 72,
78, 90 HW-WS 13 (Worksheet) (from course website)
Lab Wednesday/Thursday – EXP 10
Prelab Bring a computer if you have one
Next Monday/Tuesday – Open office hour Next Wednesday/Thursday – EXP 11
Prelab
Ejected ElectronsOne photon at the threshold frequency gives the
electron just enough energy for it to escape the atombinding energy, f
When irradiated with a shorter wavelength photon, the electron absorbs more energy than is necessary to escape
This excess energy becomes kinetic energy of the ejected electron
Kinetic Energy = Ephoton – Ebinding
KE = hn − f
1. No electrons would be ejected.2. Electrons would be ejected, and they would have
the same kinetic energy as those ejected by yellow light.
3. Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.
4. Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
1. No electrons would be ejected.2. Electrons would be ejected, and they would have
the same kinetic energy as those ejected by yellow light.
3. Electrons would be ejected, and they would have greater kinetic energy than those ejected by yellow light.
4. Electrons would be ejected, and they would have lower kinetic energy than those ejected by yellow light.
Suppose a metal will eject electrons from its surface when struck by yellow light. What will happen if the surface is struck with ultraviolet light?
3
SpectraWhen atoms or molecules absorb energy, that
energy is often released as light energyfireworks, neon lights, etc.
When that emitted light is passed through a prism, a pattern of particular wavelengths of light is seen that is unique to that type of atom or molecule – the pattern is called an emission spectrumnon-continuouscan be used to identify the material
Examples of Spectra
The Bohr Model of the Atom The energy of the atom is quantized, and the amount of
energy in the atom is related to the electron’s positionquantized means that the atom could only have very specific
amounts of energy The electron’s positions within the atom (energy levels) are
called stationary statesEach state is associated with a fixed circular orbit of the electron
around the nucleus.The higher the energy level, the farther the orbit is from the nucleus.
The first orbit, the lowest energy state, is called the ground state.The atom changes to another stationary state only by absorbing or
emitting a photon.Photon energy (hn) equals the difference between two energy states.
The Bohr Model of the Atom
nucleus
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12345
--
- -
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Emission Spectra
Bohr Model of H Atoms
Emission Spectra
Hydrogen Energy Transitions
nucleus1234
5
6
Which is a higher energytransition?
65 or 32
53 or 31
23 or 34
7
2 2
1 1.0968 10 1 1 1 2056875
4 2m m
Rydberg’s Spectrum Analysis Rydberg developed an equation involved an inverse square
of integers that could describe the spectrum of hydrogen.
1 22 2
1 1 1R
n n
What is the wavelength (nm) of light based on an electron transition from n = 4 to n = 2?
7
2 2
1 1.0968 10 1 1
4 2m
HUH?!?!?
7
2 2
1 1.0968 10 1 1 1 2056875
4486
2m m
nm
71.096776 10R
m
Wave Behavior of Electrons de Broglie proposed that particles could have wave-like
character Predicted that the wavelength of a particle was inversely
proportional to its momentum Because an electron is so small, its wave character is
significant
hλ =
mv
hcE =
2E = mc
2hc = mc
h
= mc
h = planks constant
J s2
2s
kg m
s
m = mass of particle v = velocity
kgm
s
What is the wavelength of an electron traveling at 2.65 x 106 m/s. (mass e- = 9.109x10-31 kg)
hλ =
mv
23410
31 6
6.626 10λ = 2.745 10
9.109 10 2.65 10
kg ms
ms
mkg
Determine your wavelength if you are walking at a pace of 2.68 m/s. (1 kg = 2.20 lb)
234366.626 10
λ = 2.96 1091.8 2.68
kg msms
mkg
The matter-wave of the electron occupies the space near the nucleus and is continuously influenced by it.
The Schrödinger wave equation allows us to solve for the energy states associated with a particular atomic orbital.
The square of the wave function (Y2) gives the probability density, a measure of the probability of finding an electron of a particular energy in a particular region of the atom.
The Quantum Mechanical Model of the Atom
2 2 2 2
2 2 2, , Ψ , , Ψ
8 e
h d d dV x y z x y z E
m dx dy dz
Ψ ΨH E
Probability & Radial Distribution Functions y2 is the probability density
the probability of finding an electron at a particular point in space decreases as you move away from the nucleus
The Radial Distribution function represents the total probability at a certain distance from the nucleus maximum at most probable radius
Nodes in the functions are where the probability drops to 0
Probability Density FunctionThe probability density function represents the total probability of finding an electron at a particular point in space
Radial Distribution Function
The radial distribution function represents the total probability of finding an electron within a thin spherical shell at a distance r from the nucleus
The probability at a point decreases with increasing distance from the nucleus, but the volume of the spherical shell increases
The net result is a plot that indicates the most probable distance of the electron in a 1s orbital of H is 52.9 pm
Solutions to the Wave Function, YCalculations show that the size, shape, and
orientation in space of an orbital are determined to be three integer terms in the wave function
These integers are called quantum numbersprincipal quantum number, nangular momentum quantum number, lmagnetic quantum number, ml
Principal Quantum Number, n Characterizes the energy of the electron in a particular
orbital and the size of that orbital corresponds to Bohr’s energy level
n can be any integer 1 The larger the value of n, the more energy the orbital has The larger the value of n, the larger the orbital
Greater relative distance from the nucleus As n gets larger, the amount of energy between orbitals gets
smaller Energies are defined as being negative
an electron would have E = 0 when it just escapes the atom
The energies of individual energy levels in the hydrogen atom (and therefore the energy changes between levels) can be calculated.
2
1nE hcR
n
What is the energy of a photon of light based on an electron transition from n = 4 to n = 2?
34 8 7
4 2 2 2
6.626 10 2.998 10 1.0968 10 1 1
2 4
J s mE
photon s m
18 19
4 2 2 2
2.180 10 1 1 4.087 10
2 4
J JE
photon photon
18
4 2 2 2
2.180 10 1 1
2 4
JE
photon
2 2
1 1
final initial
E hcRn n
Principal Quantum Number, n
Principal Energy Levels in Hydrogen
Angular Momentum Quantum Number, l The angular momentum quantum number determines the
shape of the orbital l can have integer values from 0 to (n – 1) Each value of l is called by a particular letter that designates
the shape of the orbitals (spherical) orbitals are sphericalp (principal) orbitals are like two balloons tied at the knotsd (diffuse) orbitals are mainly like four balloons tied at the knotf (fundamental) orbitals are mainly like eight balloons tied at the
knotprincipal (n) quantum number possible angular momentum (l) quantum number(s)
1 0 (s)
2 0, 1 (s, p)
3 0, 1, 2 (s, p, d)
4 0, 1, 2, 3 (s, p, d, f)
5 0, 1, 2, 3, 4 (s, p, d, f, g)
Magnetic Quantum Number, ml
The magnetic quantum number is an integer that specifies the orientation of the orbitalthe direction in space the orbital is aligned relative to
the other orbitalsValues are integers from −l to +l
including zeroGives the number of orbitals of a particular shape
when l = 2, the values of ml are −2, −1, 0, +1, +2; which means there are five orbitals with l = 2
