Quantum Mechanics

Directly observing electrons in the atom is impossible, the electron is

so small that observing it changes its behavior

The quantum-mechanical model explains the manner electrons exist

and behave in atoms

The model also helps us understand and predict the properties of

atoms that are directly related to the behavior of the electrons

Why study EMR?

Scientists determined in the early 20th

century that the position and

momentum of an electron can be

accurately described by wave

equations

The Nature of Light

The electromagnetic radiation composed of perpendicular oscillating

waves, one for the electric field and one for the magnetic field

All electromagnetic waves move through space at the same constant

speed of 3.00 108 m/s. This velocity is represented by ‘c’.

The Wavelength

The peak-to-peak distance is called the wavelength. The

wavelength is represented by the symbol .

Wavelength is usually expressed in units of meters, centimeters

or nanometers (1 nm = 10 – 9 m) (also Angstroms=1x10-10m)

Blue light (high energy) has shorter wavelengths and red light

has longer wavelengths (low energy)

The Energy and the Wavelength

The Frequency

Frequency () is the number of waves that pass any

reference point per unit of time or waves/time.

Frequency is measured in

hertz (Hz).

1 Hz = 1 s-1

The frequency can be calculated

from the velocity and the and the

wavelength of the radiation.

λ

cv

Different colors are attributed to the difference in wavelengths of light,

and the magnitude of brightness is directly proportional to the amplitude.

The Amplitude

Amplitude is the vertical distance from the midline of a wave

to the peak or trough. Amplitude affects the intensity or the

brightness of the radiation.

http://id.mind.net/~zona/mstm/physics/waves/introduction/introductionWaves.html

The color of light is determined by

its wavelength or frequency.

When an object absorbs some

of the wavelengths of white

light while reflecting others, it

appears colored, the observed

color is predominantly the

colors reflected.

An object appears red because it is predominantly reflecting red

light while absorbing most other colors.

The Electromagnetic spectrum

The electromagnetic spectrum is divided into regions according to

the wavelengths or the frequency of the radiation.

The Nature of Matter

End of the 19th century---Matter was

composed of particles and Energy was

composed of waves…right??

BUT

There was a problem that classical physics

couldn’t explain- that a glowing hot object

doesn’t emit UV radiation as expected……

In 1900 the German scientist Max Planck

proposed that the electromagnetic

radiation could be viewed as a stream of

tiny energy packets or quanta we now

call photons. He proposed that there is

a minimum amount of energy that can be

gained or lost by an atom

The Photons

Max Plank

(1858 – 1947)

The Photoelectric effect

Another dilemma in classical physics….

The Photoelectric Effect

It was observed that many metals emit electrons when a light shines

on their surface, this effect is called the Photoelectric Effect.

The classic wave theory attributed the photoelectric effect to the light

energy being transferred to the electron.

According to this theory, if the wavelength of light is made shorter

(higher energy) more electrons should be ejected

If a dim light was used there would be a lag time before electrons

were emitted

In experiments with the photoelectric effect, it was observed that there

was a maximum wavelength for electrons to be emitted called the

threshold frequency (regardless of the intensity).

It was also observed that high frequency light with a dim source

caused electron emission without any lag time

Einstein (1879 – 1955)

Einstein to the rescue……..

Explaimed Photoelectric Effect--

Radiant energy striking the metal

surface behaves not as a wave but as

a stream of tiny packets of energy.

Einstein (1879 – 1955)

The Energy of the Electromagnetic Radiation

Planck proposed, and Einstein

confirmed, that the energy of a photon

is proportional to its frequency.

E = h

Where is h is the Plank’s constant

and it equals = 6.626 × 10– 34 J s

This means that both electrons and electromagnetic radiation

can be represented as either waves (E) or particles (h).

Ground State and The Excited State

Atoms when exposed to electromagnetic radiation, they emit the

absorbed energy in the form of light as electrons return to a lower state.

Spectrum of ordinary white light

The visible spectrum of white light is called a continuous

spectrum, because it contains continuous distribution of all colors.

The origin of atomic line spectra is the movement of electrons between quantized energy levels

The visible line spectrum of excited hydrogen atoms consists of four

lines, from indigo at 410 nm to red at 656 nm (not a continuous

spectrum)> Each of these wavelengths represents a specific energy

transition as excited electrons move from excited states to lower energy

states

Oxygen spectrum

More examples of atomic spectra

Neon spectrum

The Energy Levels Are Quantized

Atomic line spectra tell us that when an excited atom loses energy,

not just any arbitrary amount can be lost.

This is possible if the electron is restricted to certain energy levels.

The energy of the electron is said to be quantized.

(a) Continuous energy level

(b) The energy level are

quantized.

Connected the spectra of hydrogen, and the

quantum ideas of Einstein and Planck, to explain

that single electron of hydrogen could occupy only

certain energy states

The Bohr Model

Niels Bohr(1885 -1962)

AN electron would remain in its lowest energy state until otherwise

disturbed.

The first theoretical model that successfully

accounted for the Rydberg equation was proposed

in 1913 by the Danish physicist Niels Bohr.

The Bohr Model

Niels Bohr(1885 -1962)

Bohr proposed that the electrons moved around the nucleus is

fixed paths or orbits much like the planets move around the sun.

Neils Bohr proposed that the electrons could only have very specific amounts of energy-- fixed amounts, quantized

The electrons traveled in orbits that were a fixed distance from the nucleus therefore the energy of the electron was proportional the distance the orbital was from the nucleus.

When energy is

added to an electron,

it is promoted to a

orbit further away

from the nucleus

Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy . For example they give off violet EMR when jumping from the 5 th energy level to the more stable 2nd.

Electrons emit radiation when they “jump” from an orbit with higher energy down to an orbit with lower energy . For example they give off violet EMR when jumping from the 5 th energy level to the more stable 2nd.

Bohr’s model for hydrogen atom

Bohr explained the line spectrum of hydrogen . The energies of emitted light are equal to the differences between the energy state of an electron jumping from an outer orbits and an inner orbit into which it can move

Rydberg equation

The Rydberg equation is used to calculate the energy changes when electrons are promoted to higher energy levels and subsequently fall back to the lower energy levels

In general, the line spectrum of an element is rather complicated.

The line spectrum of hydrogen, with a single electron, is the simplest.

The Rydberg equation can be used to calculated

energy levels associated with the spectral lines of

hydrogen.:

E= -2.178 x 10-18 J Z2

n2

Bohr’s calculation of the energy levels of a hydrogen atom

–energy of a particular energy level

n= Energy level

The Rydberg constant, R, is an empirical constant with a value of

-2.178 x 10-18 J/atom

Z= nuclear charge aka the number of protons

Rydberg equation

Energy changes during transitions are proportional to (atomic #). This means that if an electron is promoted from for example level 1 to level 5 in a species that has less protons in the nucleus the same transition for a species with more protons would be more difficult. This is because the protons in the nucleus are attracting the electron to the lower energy level and more energy is required to promote them.

Calculate the energy of the n=3 state of the H atom in joules perAtom

-2.421x10-19J

Calculating the delta energy between two quantized orbits

Example Problem 1: Calculate the energy involved when an electron transitions from n=1 to n=3.

+1.936 x 10─18 J NOTE: energy is positive, therefore process is endothermic, energy is required for the transition transition an absorption process!

Calculate the energy involved for an electron to transition from n=5 to n=2 for an atom of hydrogen. Does this represent absorption or emission?

  

Calculate the wavelength of light observed for the transition in the previous problem.

 

The Lyman series of spectral lines for the H atom occurs in theultraviolet region. They arise from transitions from higher levelsto n=1. Calculate the frequency and wavelength of the leastenergetic line in this series.

Answer:E = -Rhc (1/1 2 1/22) = -2.179x10-18J/atom (1/1 – 1/4) = -1.634x10-18JE = hν ν = 1.634x10-18 / 6.626x10-34Js = 2.466x1015Hzλ = c/ν = 3.00x108m/s / 2.466x1015Hz = 1.216x10-7m = 121.6nm