the model of the atom

7/27/2019 The Model of the Atom

1/22

The Model of the Atom

www.utoronto.ca www.sparknotes.com


2/22

What Does an Atom LookLike?

The question was asked by manyscientists at the turn of the century.

Electron discovered by J.J. Thomson(1897).

Scientists generally agreed that the atomwas a basic building block that all matterwas comprised of.

An atom could not be an indivisibleparticle.


3/22

J.J. Thompson (1898)

Predicted that there were massive positivelycharged particles in the atom that were offset bymuch smaller negatively charged particles.

Negatively charged particles were distributedthroughout a sea of positive charge such thatthey offset one another.

His model was known as the plum-pudding

model.

wps.prenhall.com


4/22

Earnest Rutherford (1911)The Gold Foil Experiment

Bombarded gold foil with particles fromthe radioactive decay of uranium238.

Most of the particles traveled throughvery thin gold foil without being deflected.

Occasionally, particles would deflect,sometimes at angles > 90o (due to acoulombic repulsive force).

Results show that the dense positivecharge is centrally located in the nucleus.

His model is know as the nuclear model

and disproved Thomsons theory.


5/22

The Gold Foil Experiment

Rutherford's Gold Foil Experiment

wps.prenhall.com

Note: The diameter of the atom was determined to be on

the order of 100,000x larger than the nucleus!
http://micro.magnet.fsu.edu/electromag/java/rutherford/http://micro.magnet.fsu.edu/electromag/java/rutherford/


6/22

Problems with the NuclearModel

Electrons are under constant acceleration due tocentripetal motion.

It was then reasoned that they must be giving

off EM radiation.

Conservation of energy then suggests that theelectrons would eventually spiral into thenucleus.

In addition, as the electrons got closer to thenucleus, their speed would increase as would thefrequencies of emitted radiation, covering abroad range of the EM spectrum.


7/22

Neils Bohr (1913)

1. Assumed the laws of electromagnetism do notapply inside an atom. Consequently, anorbiting electron would not lose energy even

though it is accelerating.2. Only certain orbital radiuses are possible for an

electron, representing an energy state (mvr =nh/2).

3. Energy is emitted or absorbed when

electrons change from one discrete energylevel to another. Energy levels are consistent with Einsteins theory on

the photoelectric effect where he said that photonshave discrete amount of energy (E = hf).


8/22

The Bohr Model of the Atom

Atoms have discrete energy levels associatedwith changes in location of electrons within theatom. The lowest energy level is called theground state(All

electrons are in their proper orbitals). When an atom is not in the ground state, it is

considered to be in anexcited state. When an electron absorbs energy from a photon of

light, it can transition to another discrete energy level ifthe energy of the photon is exactly equal to the

difference in energy levels. Orbits near the nucleus have less energy than those

farther out because it takes more energy to move anelectron further away.

Note: An atom is in the excited state for a very shortperiod of time (~10-9 sec.)!


9/22


10/22

In Bohr model, the centripetal force of theelectron is offset by the electrostatic force.

Fc = Femv2 kq2

r r2

Bohr said that the angular

momentum of the electron

is quantized as follows.

Ln = mvnrn = nh/2 (2)

Einstein & Bohrs TheoriesCombined (The Bohr Radius)

+

-

Fc

v= (1)

Coulombs Law


11/22

Einstein & Bohrs TheoriesCombined (The Bohr Radius)

Solving (2) for vn and substituting into (1) results in:

h2 n2

42mkq2 Z

E = KE + EPE

E = mv2 - kq2/r = -kq2/r (4)

Substituting (3) into (4) yields:

22mkq4 Z2

h2 n2

Substituting for m, k, h and q yields:

En = (-2.18 x 10-18J)Z2/n2 or En = (-13.6 eV)Z2/n2

rn = n = 1, 2, 3, (3)

+

-

Fc

v

En = (5)

AtomicNumber


12/22


13/22

+

Ei

Ef

Bohr Model and EmissionSpectra

Bohrs theory for the structure of the atom took intoconsideration Einsteins theory of photons and energy as ameans to explain why Hydrogen emits only four differentwavelengths of visible light.

Bohrs model predicts that photons of energy will beemitted in the form of EMR when an electron transitionsfrom a higher energy level to a lower energy level.

-

-

Photon emitted contains a

discrete amount of energy that isspecific to the transition.

Ei Ef= hf

Ei Ef= hc/

Bohr Atom and Emission of Light
http://webphysics.davidson.edu/physlet_resources/gustavus_physlets/emissioninbohrtheory.htmlhttp://webphysics.davidson.edu/physlet_resources/gustavus_physlets/emissioninbohrtheory.html


14/22

Visible Spectrum of theHydrogen Atom

The photons of light emitted when going from any energylevel to the ground state emit EMR in the ultravioletregion.

The photons of light

emitted when going from

other energy levels to the

2nd energy level will emit

light in the visible light

region.+

n=3

n=2

n=1

n=4

n=5

Red

655nm

blue green

485nm

Violet

409nm

Dark Blue

433nm


15/22

The Energy Levels of theHydrogen Atom (The Well)

In order for an electron to changefrom a lower energy state to ahigher energy state, the incidentphoton must have the exact

amount of energy equivalent tothe difference in energy levels ofthe hydrogen atom.

Ephoton = Ei Ef For example: an electron

transitioning from the groundstate (n=1) to a higher energylevel (n=2) requires a photon of10.2eV. What would happen if a

photon had only 10eV ofenergy of energy?

NOTHING!


16/22

Quantization of the EnergyLevels of the Hydrogen Atom

Ephoton = Ei Ef While an electron in a hydrogen

atom transitions from n=1 to n=3it needs a photon with exactly

12.09eV (13.60eV 1.51eV) ofenergy, how will it return to theground state?

When transitioning back to theground state, the electron cantake one of 3 possible transitions:3 1, or 3 2 followed by 2 1. Each jump would emit a photon

with an amount of energy equalto the difference between the twoenergy levels.


17/22

Problems with the BohrPlanetary Model

1. The Bohr model of the atom works forHydrogen, but not for other elements.

2. Bohr could not explain the conflictbetween acceleration of a chargedparticle (e-) and the production of EMradiation that would lead to the collapse

of the atom.3. Bohr could not explain the reason for

quantization of angular momentum.


18/22

Angular Momentum Solved

Bohr proposed that the angular momentum is quantized.

Ln = mvnrn = nh/2 (1)

But why should Ln be limited to values of h/2? Louis de Broglie proposed that particles travel in waves,

even in their orbits.

Electrons traveling in orbits

create standing waves

superimposed on a Bohr orbit.

Since = h/mv (2)

Where = de Broglie wavelength

Substituting (2) into (1) yields n = 2rParticle-Wave Applet
http://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c241/D1-part2.htmlhttp://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c241/D1-part2.htmlhttp://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c241/D1-part2.htmlhttp://artsci-ccwin.concordia.ca/facstaff/a-c/bird/c241/D1-part2.html


19/22

Quantum Model (HeisenbergUncertainty Principle) - 1926

Erwin Schroedinger and Werner Heisenberg developeda theoretical framework that established a new branchof physics called quantum mechanics.

Their theories explain the probability of determining aparticles position and momentum at the same time.

y=uncertainty of a particles position in the y-direction

py=uncertainty of the y-component of linear momentum

( )( )4

y

hp y

Note: it is not possible to determine theposition and momentum of an electron at

the same time!


20/22

Quantum Model (HeisenbergUncertainty Principle) - 1926

The quantum model predicts theprobabilityoffinding the electron around the nucleus of aatom.

The probability of finding an electron is itshighest in a region called the electron cloud.

www.sparknotes.com

Electron Cloud


21/22

Key Ideas

The atom is defined as a probability cloud ofelectrons with a centrally located nucleus.

The nucleus is fractionally smaller compared to

the entire atom (1/100,000th

). J.J. Thompson developed the first working model

of the atom the plum-pudding model.

Earnest Rutherford developed thenuclear/planetary model of the atom as a resultof the gold foil experiment.

Neils Bohr further developed the planetarymodel of the atom and solved many questionsabout the hydrogen atom.


22/22

Key Ideas

The Bohr model of the hydrogen atom containselectrons which orbit the nucleus in orbits thatare associated with discrete energy levels.

Erwin Schroedinger and Werner Heisenbergdeveloped the quantum model of the atom withthe wave-particle theory.

An electron in any state other than the ground

state is said to be excited. When an electron transitions from an excited

state to the ground state, it will emit a photon oflight and vice-versa when going from the ground

state to an excited state.

the model of the atom

Documents