The Nature of Light: Its Wave NatureLight is a form of

made of perpendicular waves, one for the electric field and one for the magnetic field

All electromagnetic waves move through space at the same, constant speed

Characterizing WavesThe amplitude is the

Characterizing Waves

Characterizing WavesThe wavelength (l) is

The frequency (n) is the

Characterizing Waves

LIGHT!!!wavelength and frequency are proportional

wavelength frequency

wavelength and energy are proportional

wavelength energy

energy and frequency are proportional

energy frequency

Wavelength and FrequencyWavelength and frequency of electromagnetic

waves are inversely proportional because the speed of light is constant, if we know wavelength we

can find the frequency, and vice versa

Calculate the wavelength of red light (nm) with a frequency of 4.62 x 1014 s−1

Calculate the wavelength (m) of a radio signal with a frequency of 106.5 MHz

Color The color of light is determined by

a spectrum RedOrangeYellowGreenBlueViolet

When an object absorbs some of the wavelengths of white light and reflects others, it appears colored

Types of Electromagnetic Radiation• Electromagnetic waves are classified by their wavelength

Radio waves = > 0.01 m4 2Microwaves = 1 10 m < < 1 10 m

Infrared (IR)5 4far IR = 1 10 m < < 1 10 m

6 5middle IR = 1 10 m < < 1 10 m 7 6near IR = 1 10 m < < 1 10 m

7 7Visible light = 4 10 m < < 8 10 m

Ultraviolet (UV)7 7near UV = 2 10 m < < 4 10 m

8 7far UV = 1 10 m < < 2 10 m 10 8X-rays = 1 10 m < < 1 10 m

10Gamma rays = < 1 10 m

InterferenceThe interaction between waves is called

When waves interact so that they add to make a larger wave it is called waves are

InterferenceThe interaction between waves is called

interferenceWhen waves interact so they cancel each other it is

called waves are

Diffraction When traveling waves encounter an obstacle or opening in

a barrier that is about the same size as the wavelength, they bend around it – this is called

Diffraction When traveling waves encounter an obstacle or opening in a

barrier that is about the same size as the wavelength, they bend around it – this is called diffraction traveling particles do not diffract

The diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves An interference pattern is a characteristic of all light waves

2-Slit Interference

The Photoelectric Effect It was observed that many metals emit electrons when a

light shines on their surface this is called the

Classic wave theory attributed this effect to the light energy being transferred to the electron

According to this theory, if the wavelength of light is made shorter, or the light waves’ intensity made brighter, more electrons should be ejected remember: the energy of a wave is directly proportional to its

amplitude and its frequency this idea predicts if a dim light were used there would be a lag time

before electrons were emitted to give the electrons time to absorb enough energy

Experiments showed that there was

called the

It was also observed that high-frequency light from

a dim source caused electron emission

The Photoelectric Effect: The Problem

Einstein’s ExplanationEinstein proposed that the light energy was

The energy of a photon of light is

the proportionality constant is

Calculate the number of photons in a laser pulse with wavelength 337 nm and total energy 3.83 mJ

What is the frequency of radiation required to supply 1.0 x 102 J of energy from 8.5 x 1027 photons?

Ejected ElectronsOne photon at the threshold frequency gives the

electron just enough energy for it to escape the atom

When irradiated with a shorter wavelength photon, the

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?

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

The Bohr Model of the Atom The energy of the atom is ______________, and the amount

of energy in the atom is related to the electron’s positionquantized means

The electron’s positions within the atom (______________) are called stationary statesEach state is associated with a fixed circular orbit of the electron

around the nucleus.The higher the energy level, ________________________________

The first orbit, ______________________________________________The atom changes to another stationary state only by absorbing or

emitting a photon.Photon energy (hn) equals the difference between two energy states.

nucleus12345

Bohr Model of H Atoms

Emission Spectra

nucleus

Which is a higher energytransition?

65 or 32

53 or 31

23 or 34

Rydberg’s Spectrum Analysis Rydberg developed an equation involved an inverse square

of integers that could describe the spectrum of hydrogen.

What is the wavelength (nm) of light based on an electron transition from n = 4 to n = 2?

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

What is the wavelength of an electron traveling at 2.65 x 106 m/s. (mass e- = 9.109x10-31 kg)

Determine your wavelength if you are walking at a pace of 2.68 m/s. (1 kg = 2.20 lb)

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,

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

Probability & Radial Distribution Functions y2 is the probability density

The Radial Distribution function represents the total probability at a certain distance from the nucleus

Nodes in the functions are where

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

Principal Quantum Number, n Characterizes the energy of the electron in a particular

orbital and ______________________________ corresponds to Bohr’s energy level

n can be

The larger the value of n, The larger the value of n,

As n gets larger,

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.

What is the energy of a photon of light based on an electron transition from n = 4 to n = 2?

Principal Quantum Number, n

Principal Energy Levels in Hydrogen

Angular Momentum Quantum Number, l The angular momentum quantum number determines the

_____________________________________ l can have ________________________________ Each value of l is called by a particular letter that designates

the shape of the orbital____________ orbitals are spherical____________ orbitals are like two balloons tied at the knots____________orbitals are mainly like four balloons tied at the knot____________ orbitals are mainly like eight balloons tied at the knot

principal (n) quantum number possible angular momentum (l) quantum number(s)

1

2

3

4

5

Magnetic Quantum Number, ml

The magnetic quantum number is an integer that specifies the the direction in space the orbital is aligned relative to the

other orbitals

Values are

Gives the number of orbitals of a particular shapewhen l = 2,

l = 0, the s orbital

Each principal energy level has one s orbital

_________________orbital in a principal energy state

Number of nodes = (n – 1)

l = 1, p orbitals Each principal energy state

Each of the three orbitals points along a different axis

px, py, pz

2nd lowest energy orbitals in a principal energy state Two-lobed One node at the nucleus, total of n nodes

l = 2, d orbitals Each principal energy state above

Four of the five orbitals are aligned in a different plane

the fifth is aligned with the z axis,

3rd lowest energy orbitals in a principal energy level Mainly four-lobed

one is two-lobed with a toroid Planar nodes

higher principal levels also have spherical nodes

2zd2 2xy yz xz x yd , d , d , d

l = 2, d orbitals

l = 3, f orbitals Each principal energy state above

4th lowest energy orbitals in a principal energy state Mainly eight-lobed

some two-lobed with a toroid Planar nodes

higher principal levels also have spherical nodes

l = 3, f orbitals

Quantum Numbers: n, l, ml

Quantum NumbersGive the name, magnetic quantum numbers, and number of orbitals for each sublevel with the following quantum numbers:

(a) n = 3, l = 2

sublevelname

possible ml

valuesnumber of

orbitals

(b) n = 2, l = 0

(c) n = 5, l = 1

(d) n = 4, l = 3