Download quantum number - Reseda High School

C.F.
1 MOLE : 6.02 x 1023 ATOMS
Question gives
you moles and
asks for number
of atoms
Question gives
you number of
atoms and ask
for moles
C.F.
1 MOLE : Molar Mass in
Grams
Question gives
you moles and
asks for grams
Question gives
you grams and
asks for moles
C.F. Molar Mass = MOLE = 6.02 x 1023 atoms
Question gives you grams and asks for number
of atoms
1. Convert grams to Moles
2. Convert moles to # of atoms
C.F. 6.02 x 1023 atoms =
MOLE = Molar
Mass
Question gives you number of atoms and asks
for mass in grams
1. Convert # of atoms to moles
2. Convert moles to grams
INSTRUCTIONS
1. Draw sideways T
2. Write your “given” in the first box
If you are given GRAMS:
1. Use Periodic Table to find molar mass of element.
2. Solve
1. Use “6.02x 1023
2. Solve
If you are given # OF ATOMS
atoms”
INSTRUCTIONS
1. Draw sideways T
2. Write your “given” in the first box
1.
2.
3.
4.
5.
6.
7.
If you are given GRAMS:
Write “1 mole” in the next top box.
Then write the molar mass in the opposite
corner.
Solve for mole.
Convert mole to number of atoms by:
Write “6.02 x 1023 atoms” in the next top box
Then write “1 mole” in the opposite corner
Solve
INSTRUCTIONS
1. Draw sideways T
2. Write your “given” in the first box
1.
2.
3.
4.
5.
6.
If you are given GRAMS:
Find molar mass using periodic table and write in the opposite corner.
Write “1 mole” in the box above.
Convert mole to number of atoms by:
Then write “1 mole” in the opposite corner
Write “6.02 x 1023 atoms” in the box above
Solve
If you are given # OF ATOMS
1.
2.
3.
4.
5.
6.
Then write “6.02x 1023 atoms” in the opposite corner.
Write “1 mole” in the box above.
Convert mole to grams by:
Then write “1 mole” in the opposite corner.
Find molar mass using periodic table and write it in the box above
Solve
1. Quantum Model of the
Atom
OBJECTIVE: To understand energy, and how we
got to our present understanding of an atom
1. Quantum Model
1. Quantum Model
Wavelength: distance between two points, either crests or
troughs
1. Quantum Model
Frequency: number of waves that passes a certain point in
1 second.
1. Quantum Model
2 properties of waves
Wavelength: distance between two points, either crests or
troughs
Symbol: l
Units = meters, m
Frequency: How many waves that passes a certain point in 1
second.
Symbol: v
Units = Hz, or sec-1
INVERSE relationship between wavelength and
frequency
1. Quantum Model
2 properties of waves
Wavelength: is…
Symbol: ?
Units = ?
Frequency: is…
Symbol: ?
Units = ?
What does it mean for wavelength and
frequency to have an inverse relationship?
1. Quantum Model
Calculations using lv = c
A wave has a frequency of 4.61 x 104 Hz. What is
its wavelength in meters?
1.
2.
3.
4.
Write the equation: lv = c
Plug in values. C = 3.0 x 108 m/s ALWAYS
Rearrange equation to solve for unknown.
Solve
1. Quantum Model
Calculations using lv = c
Your favorite radio station broadcasts the signal
at 99.5 MHz. This is equal to 9.96 x 107 Hz.
Calculate the wavelength in meters.
1.
2.
3.
4.
Write the equation: lv = c
Plug in values. C = 3.0 x 108 m/s ALWAYS
Rearrange equation to solve for unknown.
Solve
1. Quantum Model
Calculations using lv = c
Photosynthesis uses light waves with a wavelength
of 660 nm to convert CO2 and H2O into glucose
and O2. 660 nm = 6.6 x 10-7m Calculate the
frequency.
1.
2.
3.
4.
Write the equation: lv = c
Plug in values. C = 3.0 x 108 m/s ALWAYS
Rearrange equation to solve for unknown.
Solve
1. Quantum Model
Answer on Warmup Paper. Label it as “WAVES”
Wavelength
Frequency
What is…
Symbol:
Unit:
Your favorite FM radio station broadcasts at a frequency of 101.1 MHz.
This is equal to 1.011 x 108 Hz. What is the wavelength of this station
in meters?
A police officer is using a radar gun for speeding citations. The gun
uses waves with a wavelength of 8.45 nanometers. This is equal to
8.45 x 10-9 meters. What is the frequency in Hz?
1. Quantum Model
Calculations using lv = c
Photosynthesis uses light waves with a wavelength of 660
nm to convert CO2 and H2O into glucose and O2. 1 nm = 1.0
x 10-9m. Calculate the frequency.
1.
2.
3.
4.
5.
Convert 660nm to meters using sideways-T
Write the equation: lv = c
Plug in values. C = 3.0 x 108 m/s ALWAYS
Rearrange equation to solve for unknown.
Solve
1. Make sure that l is in METERS, or that v is in Hz
2. If not, then convert to METERS or Hz using the
conversion factors given to you.
3. Solve: Step-by-step instructions on how to solve
should be in your notes
4. Does your final answer have the units that is
asked for in the problem?
1. Quantum Model
1. Quantum Model
X-Ray
Sunburn from UV rays
1. Quantum Model
Heat energy in
the form
of
Infrared waves
1. Quantum Model
In the 1900’s physicist thought they were able to explain
any type of phenomena.
They organized the world into two categories:
Matter
- Made up of particles
Energy
- Energy, in the
form of light,
existed as waves
1. Quantum Model
In the 1900’s physicist thought they were able to explain
any type of phenomena.
They organized the world into two categories:
Matter
-Made up of particles
- Has mass and volume
Energy
-Energy, in the
form of light,
existed as waves
- does NOT have mass
or volume
1. Quantum Model
Energy as massless
waves
1. Quantum Model
Relationship
between
ENERGY and
WAVELENGTH
1. Quantum Model
1. Quantum Model
Quantized?
Max Plank
Means that energy is gained or lost ONLY in
amounts of WHOLE NUMBERS
Means that energy is transferred in “packages”
called a QUANTUM = the smallest unit of energy
Similar Examples:
1. Musical instruments are “quantized” in that they can
only produce certain notes, like C or F#.
2. US Dollars is “quantized” in whole number multiples of
pennies.
1. Quantum Model
What does it mean for energy to be QUANTIZED?
What is a quantum? How is a penny like a quantum?
1. Quantum Model
Max Plank
E = hv
1. Quantum Model
Einstein and the Photoelectric Effect
Photoelectric Effect:
when electrons are released
from a surface of a metal
that has been exposed to light
1. Quantum Model
Einstein and the Photoelectric Effect
Why does nothing happen
when red light makes contact
with the metal?
Why does only violet light
release an electron?
1. Quantum Model
Einstein and the Photoelectric Effect
It was thought that color should not matter, only intensity
But experiment showed that color does matter.
1. Quantum Model
Einstein and the Photoelectric Effect
Einstein applied Plank’s idea, that…, to the photoelectric
effect…
1. Quantum Model
Einstein and the Photoelectric Effect
Light is also quantized
Light is a stream of particles called
PHOTONS
PHOTON: a particle of light
1. Quantum Model
Why Plank and Einstein are important
1. Quantum Model
Why Plank and Einstein are important
Plank’s and Einstein's postulate that energy is
quantized is in many ways similar to Dalton’s
description of atoms. Both theories are based on the
existence of simple building blocks, atoms in one case,
and quanta in the other. The work of Plank and
Einstein thus suggested a connection between the
quantized nature of energy and the properties of
individual atoms. In fact, Einstein's Nobel Prize was
awarded for his work in the photoelectric effect and
demonstrating its fundamental important, not for his
famous E=mc2 equation.
1. Quantum Model
Summary of Plank and Einstien
1. Energy is quantized. It can only occur in discrete
units called quanta.
2. Light, in fact the entire electromagnetic spectrum,
exists as BOTH waves and particles.
Interesting Implications – What their findings mean
1. Energy has “mass!”
2. If it has mass, then energy is a form of matter!
3. If energy, in the form of light, is both wave and
particle, then ALL MATTER exists as both waves
and particles
1. Quantum Model
In the 1900’s physicist organized the world into two
categories:
Matter
-Made up of particles
- Has mass and volume
Energy
-Energy, in the
form of light,
existed as waves
- does NOT have mass
or volume
But after Plank and Einstein’s work, we now see that
ENERGY (light) and MATTER NOT separate, but related
1. Quantum Model
What does it mean for light to be quantized?
What is a photon?
What is a quantum?
How is a photon like a quantum?
1. Quantum Model
1. Quantum Model
1. Quantum Model
1. Quantum Model
1. Quantum Model
What does it mean for
energy to be quantized?
What does it mean for
light to be quantized?
What is a quantum?
What is a photon?
How is a penny or steps on a stair like a quantum
of energy?
1. Quantum Model
Plank + Einstein = Calculating the Energy of one
Photon
E = (hc)/l
1. Quantum Model
Plank + Einstein = Calculating the Energy of one
Photon
E = (hc)/l
h = Plank’s Constant
h = 6.626 x 10-34 J•sec
This number NEVER changes
(J = Joule, the unit for measuring energy)
1. Quantum Model
Plank + Einstein = Calculating the Energy of a Photon
E = (hc)/l
The blue color in fireworks results when copper is
heated to about 1200°C. The blue light has a
wavelength of 450 nm. What is the unit of energy
emitted?
1. Write equation
2. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS
3. Solve
ANSWER = 4.42 x 10-19 J
1. Quantum Model
Plank + Einstein = Calculating the Energy of a Photon
E = (hc)/l
A ruby laser used at grocery stores to scan barcodes
emits a red light at a wavelength of 694.3 nm. What is
the energy in J? 1 nm = 1.0 x 10-9 m
1. Write equation
2. Make sure l is in METERS. Plug in values. h = 6.626
x 10-34 J•sec ALWAYS
3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS
4. Solve
1. Quantum Model
Plank + Einstein = Calculating the Energy of a Photon
E = (hc)/l
A ruby laser emits a red light at a wavelength of 694.3
nm. What is the energy in J?
1. Write equation
2. Make sure l is in METERS. Plug in values. h = 6.626
x 10-34 J•sec ALWAYS
3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS
4. Solve
ANSWER = 2.861 x 10-19 J
1. Quantum Model
Plank + Einstein = Calculating the Energy of a Photon
E = (hc)/l
An x-ray generator, such as those used in hospitals,
emits radiation with a wavelength of 1.544 angstrom.
What is the energy of a single proton?
1. Write equation
2. Make sure l is in METERS. Plug in values. h = 6.626
x 10-34 J•sec ALWAYS
3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS
4. Solve
1. Quantum Model
Plank + Einstein = Calculating the Energy of a
Photon
E = (hc)/l
1. Write equation
2. Make sure l is in METERS. If not, then convert
it to METERS using sideways T
3. Plug in values h = 6.626 x 10-34 J•sec ALWAYS
Plug in values. c = 3.0 x 108 m/sec ALWAYS
4. Solve
1. Quantum Model
Energy, Photons and Line Spectrum
1. Quantum Model
Energy, Photons and Line Spectrum
What is a line spectra?
Normal, white light,
separates into all the colors
of the visible spectrum.
1. Quantum Model
Energy, Photons and Line Spectrum
What is a line spectra?
When PURE elements are
heated using an electric
charge, they give off light.
But when that light passes
Through a prism, only a
few narrow lines of color
are seen.
1. Quantum Model
Energy, Photons and Line Spectrum
What is a line spectra?
When PURE elements are
heated using an electric
charge, they give off light.
But when that light passes
Through a prism, only a
few narrow lines of
color are seen.
1. Quantum Model
Energy, Photons and Line Spectrum
What is a line spectra?
Line Spectrum = a spectrum in which light of only
certain wavelength is emitted or absorbed, rather
than a continuous range of wavelengths.
1. Quantum Model
Energy, Photons and Line Spectrum
What is a line spectra?
1. Quantum Model
Energy, Photons and Line Spectrum
Why do we get line spectrums?
Neil Bohr said it is because
atoms have energy levels that are
QUANTIZED
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
Bohr said that electrons ORBIT the nucleus
Okay…how is this different from Rutherford’s
model?
1. Quantum Model
Bohr’s Model
Bohr said that electrons ORBIT the nucleus, and
that these orbits OCCUPY ONLY CERTAIN
REGIONS OF SPACE
ORBITS are QUANTIZED
The ORBITS represent different energy levels
These energy levels are quantized
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
Ground State = when electrons are arranged in
the most stable and lowest possible energy level.
Ground State has a value of n = 1
EXAMPLE: Standing on the lowest
step
1. Quantum Model
Bohr’s Model
Excited State = when electrons are arranged with
a higher energy level than the ground state. Not
as stable as ground state.
Excited State has a value of n
EXAMPLE: standing on any
step higher than
the first one
>1
1. Quantum Model
Bohr’s Model
Excited State = when electrons are arranged with
a higher energy level than the ground state. Not
as stable as ground state.
Excited State has a value of n
>1
HIGHER the N number, the more unstable
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Bohr’s Model
1. Quantum Model
Just like you must be ON a step and not in between steps,
electrons must also be ON a step. These steps are like
_____ levels, and Bohr called these energy levels ______.
Bohr said these orbits are ______ because electrons will
always be located in an orbit, never between.
The lowest step on stairs is like the _____ state, and any
step that is higher is like the _____ state. When you jump
off a step close to the ground, you make little noise. This is
like red light that has a long wavelength, a ____ frequency
and not much _____. When you jump off a step
that is very high, and jump to the ground, you
make a loud noise. This is like violet light that
has a shorter wavelength, a _____ frequency,
and so lots of ______.
Orbits
1.
represent…
Orbits are
quantized,
meaning…
ENTER ANSWER
Quantum
HERE Model
Bohr’s Model
ENTER
RESPONSE
HERE
Ground state =
ENTER ANSWER
HERE
n ? 1
Excited state =
ENTER
RESPONSE
HERE
n ? 1
1. Quantum Model
Bohr’s Model
3. Describe what happens when the electron falls
from an excited state to a ground state?
When an electron falls from an excited state to
the ground state, light is emitted. The color of
light depends on the change in energy levels, just
like the sound made when jumping off stairs.
Jumping off a high step makes a loud noise and has
a high frequency with high energy. Like Jenga, the
higher the block, the more sound it produces.
1. Quantum Model
Bohr’s Model
4. How does the above explain why elements have
line spectrum and not a continuous spectrum?
Elements have line spectrums instead of a
continuous spectrum because the orbits are
quantized, which means there are gaps from which
electrons cannot fall. The lines represent the color
that go with the amount of energy.
It can only be a continuous spectrum if the
electron is able to move without the orbits
1. Quantum Model
Bohr’s Model
5. How is this related to fireworks?
1. Quantum Model
Bohr’s Model
Main importance of Bohr’s Model
His main contribution: There is a connection
between the orbits of an atom and its line
spectrum.
But why are orbits only at certain levels?
1. Quantum Model
De Broglie and Standing Waves
But why are orbits only at certain levels?
De Broglie hypothesized that the electron behaves
like a standing wave
1. Quantum Model
De Broglie and Standing Waves
standing wave = a wave that does not travel
An example = a string of a violin or guitar. When
the string is plucked, it vibrates at certain fixed
frequencies because it is fastened at both ends.
1. Quantum Model
De Broglie and Standing Waves
standing wave = a wave that does not travel
NOT standing waves
1. Quantum Model
De Broglie and Standing Waves
standing wave = a wave that does not travel
1. Quantum Model
De Broglie’s idea that an electron is a s______
w____ explained Bohr’s orbits and energy levels
nicely
How?
visual demo
1. Quantum Model
De Broglie’s idea that an electron is a s______
w____ explained Bohr’s orbits and energy levels
nicely
How?
1. Quantum Model
De Broglie’s idea explained Bohr’s orbits and energy
levels nicely
lowest energy level, n = 1
one complete wavelength would close the circle
2πr = nλ
Higher energy levels would have successively
higher values of n with a corresponding number of
nodes.
n = number of nodes
1. Quantum Model
1. Quantum Model
ONE PROBLEM with De Broglie’s idea:
Because a wave is a disturbance that travels in
space, it has no fixed position. One might
therefore expect that it would also be hard to
specify the exact position of a particle that
exhibits wavelike behavior.
1. Quantum Model
ONE PROBLEM with De Broglie’s idea:
Hard to know exactly where the wave/particle is
AND
how fast it is moving
German physicist Werner Heisenberg
Uncertainty Principle:
We can know position/WHERE an electron is OR
momentum/SPEED
NOT BOTH
1. Quantum Model
So where is an electron?
We do not know!
If we know where it is, we do not know how fast it
is going
If we know how fast it is going, we do not know
where it is
CANNOT KNOW BOTH
1. Quantum Model
CANNOT KNOW BOTH
The best we can do is…
it is probably here
OR
it is probably going this fast
1. Quantum Model
Erwin Schrodinger
1. Quantum Model
Erwin Schrodinger
Plank + Einstein + Bohr + De Broglie + Heisenberg =
Schrodinger’s Quantum Model of the atom =
1. Quantum Model
Erwin Schrodinger
Plank + Einstein + Bohr + De Broglie + Heisenberg =
Schrodinger’s Quantum Model of the atom
Last model of the atom we will learn!!
1. Quantum Model
Erwin Schrodinger
Schrodinger’s Quantum Model of the atom =
Model that shows where electrons (as both a wave
and a particle) probably are in an atom
1. Quantum Model
Erwin Schrodinger
Quantum Numbers
1. Quantum Model
Erwin Schrodinger
Quantum Numbers
4 numbers that tells us where electrons most
likely are
1. Quantum Model
QUANTUM NUMBERS
1. The Principal Quantum Number
1. Quantum Model
QUANTUM NUMBERS
1. The Principal Quantum Number
The principal quantum number (n) tells the average
distance of an electron from the nucleus:
1. Quantum Model
QUANTUM NUMBERS
1. The Principal Quantum Number
The principal quantum number (n) tells the
average distance of an electron from the
nucleus:
n = 1, 2, 3, 4,…
1. Quantum Model
QUANTUM NUMBERS
2. The Angular Quantum Number
describes shape of space where electrons most
likely are.
The values of
l
= 0 to n − 1
1. Quantum Model
QUANTUM NUMBERS
2. The Angular Quantum Number
describes shape of space where electrons most
likely are.
The values of
EX: n = 1
l
= 0 to n − 1:
1. Quantum Model
QUANTUM NUMBERS
2. The Angular Quantum Number
describes shape of space where electrons most likely
are.
The values of
l
EX: n = 1,
1-n=0
So l = 0
= 0 to n − 1:
n=2
1-n=1
So l = 0, 1
n=3
1-n=2
So l = 0, 1, 2
1. Quantum Model
The Magnetic Quantum Number
The third quantum number is the magnetic
quantum number (ml). The value of ml describes
the orientation of the region in space occupied by
an electron with respect to an applied magnetic
field.
The allowed values of ml depend on the value of l:
ml can range from −l to l in integral steps:
EQUATION 6.23
ml = −l, −l + 1,…, 0,…, l − 1, lv
1. Quantum Model
QUANTUM NUMBERS
2. The Angular Quantum Number
describes shape of space where electrons most likely
are.
The values of
l
EX: n = 1,
1-n=0
So l = 0
= 0 to n − 1:
n=2
1-n=1
So l = 0, 1
n=3
1-n=2
So l = 0, 1, 2
1. Quantum Model
What is the difference between an ORBIT and an
ORBITAL?
An orbit is the exact path an electron travels.
An ORBITAL is a
1. Quantum Model
What is the difference between an ORBIT and an
ORBITAL?
1. Quantum Model
Because a wave is a disturbance that travels in
space, it has no fixed position. One might
therefore expect that it would also be hard to
specify the exact position of a particle that
exhibits wavelike behavior.
This situation was described mathematically by
the German physicist Werner Heisenberg
1. Quantum Model
the wavelike nature of subatomic
particles such as the electron made it impossible to
use the equations of classical physics to describe the
motion of electrons in atoms. Scientists needed a new
approach that took the wave behavior of the electron
into account. In 1926, an Austrian physicist, Erwin
Schrödinger (1887–1961; Nobel Prize in Physics,
1933), developed wave mechanics, a mathematical
technique that describes the relationship
between the motion of a particle that exhibits
wavelike properties (such as an electron) and its
allowed
energies. In doing so, Schrödinger developed the
theory of quantum mechanics, describe the energies
and spatial distributions of electrons in atoms and
molecules.
1. Quantum Model
As n increases for a given atom, so does the average
distance of an electron from the nucleus. A
negatively charged electron that is, on average, closer
to the positively charged nucleus is attracted to
the nucleus more strongly than an electron that is
farther out in space. This means that electrons with
higher values of n are easier to remove from an atom.
All wave functions that have the same value of n
are said to constitute a principal shell because those
electrons have similar average distances from the
nucleus. As you will see, the principal quantum number
n corresponds to the n used by Bohr
1. Quantum Model
The Azimuthal Quantum Number
For example, if n = 1, l can be only 0; if n = 2, l can
be 0 or 1; and so forth. For a given atom, all
wave functions that have the same values of both
n and l form a subshell. The regions of space
occupied
by electrons in the same subshell usually have the
same shape, but they are oriented differently in
space.
1. Quantum Model
For example, if l = 0, ml can be only 0; if l = 1, ml
can be −1, 0, or +1; and if l = 2, ml can be −2, −1,
0, +1, or +2.
Each wave function with an allowed combination of
n, l, and ml values describes an atomic orbital,