chemistry 101-wi50 lecture 2

8/3/2019 Chemistry 101-WI50 Lecture 2

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Quantum Mechanics and Atomic

Theor

An in-depth view of the atom and its

components(mainly electrons)


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Atomic Structure

(a brief introduction)

An atom consists of a small nucleus (D ~ 10-13 cm) surrounded by electrons

moving at an average distance 10-8 cm away)

The nucleus contains protons and neutrons and is very small and very

dense

The proton and neutron masses are roughly the same while electrons are

The number and arrangement of the electrons determine the properties

of the atoms

Particle Mass Charge

Neutron 1.67 x 10 -27 kg 0

Proton 1.67 x 10 -27 kg +1

Electron 9.11 x 10 -31 kg -1


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Isotopes


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Quantum Mechanics

Around two hundred years ago, scientists proposed theexistence of the atomic model (matter is made up ofbasic units).

Basic stoichiometric experiments cemented this belief.

The next logical question was what are atoms and what

are they made up of. Periodic trends can be explained by knowing about the

atoms and the electrons in the context of quantummechanics

Quantum mechanics was a brand new area of physicsthat was able to explain many of the observationsregarding electrons in the early 1900s


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Electromagnetic (EM) Radiation

Energy travels through space via electromagnetic radiation(not exclusively) Sun light

Microwave energy

X-rays

Radiowaves, etc.

All these types of energy experience wavelike behaviourand as such are characterized by: Wavelength

Frequency

Speed

The name electromagnetic is derived from the fact that ithas an electric field and a magnetic field that travelperpendicular to each other


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Describing EM radiation


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The electromagnetic spectrum

Which have higher frequency: Gamma rays orradiowaves?

Which has higher frequency: blue light or red light?

What is your perception about the energy of differentradiation?


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Example

The wavelength (colour) that humans can see best is 555 nm

(yellowish green)

Calculate the frequency this light

c = , = c/

(3.00*108

m/s) / (555 nm * 10-9

m/nm) = 5.41*1014

s-1

= 5.41*1014

Hz

Calculate the wavelength corresponding to 480 THz? What colour

does that correspond to?

480 THz = 480*1012 Hz = 4.80*1014 s-1

= c/

(3.00*108 m/s) / (4.80*1014 s-1) = 6.25*10-7 m = 625 nm

Red


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The Blackbody Experiment

About 120 years ago it was common knowledge

that matter and energy were distinct

Matter was made up of particles (molecules

atoms) that can be counted. Energy on the other

hand was described by waves. Matter had a mass

while energy was continuous and delocalized.

Experiments in the early 1900s started to prove

otherwise

One of the first experiments was considered by

Max Planck. He studied the profile intensity of EM

radiation as a body is heated to incandescence.


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The Blackbody Experiment A hot object radiates energy over a broad range

of wavelengths (frequencies). The energyradiated at a given frequency increases as the

frequency increases, reaches a maximum, then

declines as frequency increases further.

The maximum energy frequency increases as the

temperature increases, thus the color of an

incandescent object depends on its temperature.

Cooler objects are more red, while hotter objects

are white or even blue.

Classical physics had difficulty explaining the

reason for the declining emission at shorter

wavelengths. Planck suggested that EM waves cannot possess

just any frequency but only specific frequencies.

In more detail, he discovered that energy could

only be a whole number multiple of h

http://www.youtube.com/watch?v=l_t8dn4c6_g


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Quantized Energy


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Photoelectric Effect


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Practice problems - Energy and Wavelength

What is more energetic X-rays (10-10 m) or microwaves (10-2)? It takes 208.4 kJ of energy to remove one mole of electrons

from the atoms on the surface of rubidium metal. If Rb-metal

is irradiated with 254 nm light, what is the maximum KE the

released electrons can have?

(208.4 kJ/mole) / (6.022*1023 e-/mole) = 3.4606*10-22 kJ/e- =

3.4606*10-19 J/e-

E = h = hc/ = (6.626*10-34 Js * 2.998*108 m/s)/254*10-9 m =

7.8207*10-19 J

7.82*10-19 J - 3.46*10-19 J = 4.36*10-19 J


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Energy and Mass


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Summary

Energy is quantized

It can only be transferred in small packets

called quanta EM ra iation appears to ave some partic e

like properties. This effect is known as the

dual nature of light. Does matter also have

dual nature?


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Does matter exhibit wavelike properties?

EM radiation exhibits particle-like properties.

Matter exhibits both particulate and wave properties.

Big pieces of matter exhibit only particle like properties

Small pieces of matter exhibit mostly wavelike properties

Pieces of matter with an intermediate size have both properties


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Atomic Spectrum of Hydrogen

When a high-energy discharge is passed through a sample of

hydrogen gas, the H2 molecules absorb energy which causes the H-H bonds to break. The resulting atoms absorb energy (are excited),

the energy is then released by emitting light of different

wavelengths.

The white light emitted by an incandescent object has a broad

spectrum that covers all energies, but the light emitted by the

defined wavelengths are observed. The hydrogen emission

spectrum is called a line spectrum.

This suggests that there are only a select group of energies for an

electron in a hydrogen atom. In other words the electron in thehydrogen atom is quantized.


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(nm)


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The Bohr Model

Niels Bohr developed a quantum model for the H atom which was looselybased upon the orbits the planets in our solar system

Each energy level was found to correspond to a specific orbit for theelectron about the nucleus.

Each orbit, or principal quantum number n, where n = 1 is the lowestenergy level (ground state), n = 2,3,4,5,etc. are excited states and n = is thepoint at which the electron and the nucleus no longer interact (i.e. theelectron has been promoted completely out of the atom).


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Bohr Model


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Bohr model

Compare the energy when theelectron is closest to the nucleus towhen the electron is ionized

The lowest energy of the electronis called the ground state

Calculate the energy when thee ectron is in eve 4

Calculate the energy when theelectron is in level 1

Calculate the change in energy asthe electron moves from level 4 to

level 1. Does the sign make sense What wavelength corresponds to

this energy?


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Electronic Transitions


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Example

An excited hydrogen atom emits light with a wavelength of397.2 nm to reach the energy level for which n = 2. In whichprincipal quantum number did the electron begin?

E = h = hc/ = (6.626*10-34 Js * 2.998*108 m/s) / 397.2*10-9

m = 5.0012*10-19 J

E = -2.178*10-18 J * (1/n2 1/22)

5.0012*10-19 J / -2.178*10-18 J = -0.22962 = (1/n2 1/4)

-0.22962 + 0.25 = 0.020376 = 1/49 = 1/72

n = 7


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Example

Consider an electron for a hydrogen atom in an excited state.The maximum wavelength of electromagnetic radiation thatcan completely remove (ionize) the electron from the H atomis 1460 nm. Determine the initial excited state for theelectron?

E = h = hc/ = (6.626*10-34 Js * 2.998*108 m/s) / 1460*10-9 m= 1.360599*10-19 J

E = -2.178*10-18 J * (0 1/n2)

1.360599*10-19 J / -2.178*10-18 J = -0.062470 = (-1/n2)

0.062470 = 1/16 = 1/42

n = 4


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What about other atoms than hydrogen?


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The Quantum Mechanical Description of the

Atom

Heisenberg, de Broglie and Schrdinger contributed to develop a new

atomic model that works for all atoms (unlike the Bohr model).

The approach developed by de Broglie and Schrdinger became known as

wave mechanics or quantum mechanics.

de Broglie showed that electrons can behave like waves (remember

diffraction patterns?)

To Schrdinger and de Broglie the electron bound to the nucleus seemed

like a standing wave.


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Standing Waves Standing waves are found in guitars, violins,

etc.

A string attached at both ends

The dots are called the nodes. They are the

points of zero movement of the waves

de Broglie and Schrdinger demonstrated

that there are only some circular orbits with

a circumference that into which a wholewave engt w t

Other orbits produce destructive

interference and do not exist

This observation provides an explanation for

the quantization of energies in the hydrogenatom


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The Schrdinger Equation


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The Heisenberg Uncertainty Principle


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Example

Calculate the minimum uncertainty in position for:

an electron with v = 0.100 m/s

how does this number relate to the size of an atom?

a chemistry instructor (m = 65 kg, v = 10 km/h, uncertainty

in velocity is 0.1 km/h)

how does this number relate to the size of an instructor?

chemistry 101-wi50 lecture 2

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