Models of the Atom

Models of the Atom

1907 Plum Pudding Model - Thomson

Rutherford Model 1911

Ernest Rutherford “atoms contain a very small heavy central positive nucleus, with the e-orbiting randomly around.

Alpha particles are He nuclei 2p+, and 2no.

2 elementary charges.

Most particles went straight through, but the ones that passed closest the Au nucleus were progressively more deflected.

Gold foil experiment :atom is mostly empty space

with dense positively charged nucleus.

Neg e- move in circular orbits about the +nucleus.

e- attracted to nucleusby electrostatic F

-inertia from circular velocity of e- (angular momentum) balanced the electrostatic attraction of the nucleus.

What kept the neg e- from fall into the nucleus?

+

Problems:

• James Maxwell had proved earlier that accelerated charges radiate EM energy.

• Since e- is in circular motion it is accelerated.

• e- should lose E & spiral into the nucleus.

• That does not happen!

• Also - How did positive nucleus stay together?

One interesting discovery of Rutherford’s experiment was he could estimate the diameter of the nucleus.

He was able to use the repulsion of the alpha particle & the angle of deviation to estimate the diameter of the gold nucleus.

Angle of Deflection

The particle repelled straight back would have to come to rest for a moment. At that moment its KE would be balanced by electrical PE.

Angle of deviation from undeflected path. Rutherford used scattering angles from many

particles to make his measurement.

KE = E elc.

KE = kQq/r

• Q = charge on nucleus

• q = charge on alpha particle

• r is the “distance of closest approach”

see table p 8 topic 9 V = kq/r.

Ex 1: An particle with KE = 7.7 MeV aimed at a gold nucleus is repelled straight back. Find the

distance of closest approach.

• 3 x 10-14 m.

• IB Questions Rutherford.

Bohr proposed working model for H.

• e- circles nucleus.

• Fc provided by Felc keeps e- in orbit.

• Only orbits with certain radii allowed.

• Larger radius orbits require more e- energy for e- to occupy.

• Electrons jump between orbits somehow without occupying space between.

• Take “Quantum Leap”

• Ground state = lowest possible e- energy.

• Electrons emit photons of E, when falling to ground.

• Electrons absorb photons of E, when jumping to higher/larger radii orbits.

• Since E conserved, E emitted as photon of EM as e- falls.

• E = Ef – Ei = hf.

Evidence for Bohrcomes from emission and absorption spectra of light.

Electric E supplied to gas tubes causes gases to emit light.

Emission SpectrumWhen viewed through a prism or

spectroscope, we see only certain of light are emitted by each element.

Bright Line Spectra

Continuous spectrumFrom sunlight

Frequencies emitted exactly match the frequencies absorbed.

Quantization

• Since e- can only occupy certain orbits, the orbits themselves are quantized!

• To “jump” to a higher orbit, an e- absorbs an exact amount of energy equivalent to the difference between the E of the two orbits.

• If the E is more than the difference, no jump will occur.

• Light is produced during e- transitions.

• It is not continuous but quantized in packets – photons.

• A beam of light is made of trillions of photons produced from e- transitions.

• More photons = brighter light.

• Think of higher f photon as more massive – higher momentum.

Summary

Diagrams

Orbital Energy Levels/ Ionization Energy

Each orbit is associated with a specific energy which corresponds to the minimum energy needed to totally strip an e- from that orbit.

This ionization energy is more than the energy needed to jump between orbits.

If an atom absorbs E equal to the orbit E it becomes ionized (charged).

Orbits are named by quantum number/letter.

Ex 2: How much energy would be needed to ionize an electron:

In the n=1 level of of Hydrogen?

in the n = b or level of Mercury?

In the n = 2 level of Hydrogen?

Atoms must also absorb energy for the e- to jump to higher orbits.

The amount of energy needed to jump up must exactly equal the E difference btw orbits.

Ephoton = Ei - Ef

Use Ephoton = hf of the radiation.

to find frequency associated with photon of known energy.

Ex 3: a) How much E is absorbed when a H e- jumps from n=1 to n=3?

B) If the e- drops back down to the n=1 orbit, what f photon is emitted?

C) To which type of radiation does that photon correspond?

D) How many different photons are possible to be emitted by electron dropping from the n=3 to n=1 level?

n =3 to n = 1 Ephoton = Einitial - Efinal.

-13.6 eV - (-1.51 eV)= -12.1 eV

(12.1 eV)(1.6 x 10-19 J/eV) = 1.936 x 10-18J.

E = hf. f = E/h

f = 1.936 x 10-18J/(6.63 x 10-34 Js)

f = 2.92 x 1015 Hz. Look up.

Ex 4: A Mercury Atom has an e- excited from the n=a to the n=e energy level.

• What is the frequency it will absorb?

• To which radiation does the frequency correspond?

• If the e- drops down from the e to the b level, what type of radiation will it emit.

Homework Set

• Read Hamper 7.1 pay attention to purple box. Do 1 – 4 page 149 and

• IB packet Bohr Model prb

Hist of Quantum pt 1 British 15 min Max Planck and E= hf.

• http://www.youtube.com/watch?v=zBTbqOgdfEY

Bohr Model 6 min

• http://www.youtube.com/watch?v=-YYBCNQnYNM&feature=player_detailpage#t=101s

Go to Matter WavesNext PPT

Einstein realized that matter contains energy. There is an equivalence of mass & energy.Energy is stored in the nucleus of atoms.

The energy stored any mass obeys Einstein’s equation:

E = energy in J.E = mc2. m = mass kg

c = vel of light

Ex 2: How much energy is produced when 2.5 kg of matter are completely converted to energy?

How much energy is that in eV?

E = mc2.

=(2.5 kg )(3x108 m/s)2. = 2.25 x 1017 J

in eV

(2.25 x 1017 J)(1 eV / 1.6 x 10 –19 J) = 1.4 x 1036 eV.

Atomic Mass Units: amu or u

• Mass of atoms very small so they are measured in amu or u.

• Since mass is equivalent to energy,

• 1 amu = 931 MeV or 931 x 106 eV.

Ex 3: One universal atomic mass unit is equivalent to an energy of 931 MeV. Calculate the mass in kg of one universal mass unit.

Hint: Use E = mc2 where energy is known in eV.

Don’t forget to convert MeV to eV.

(1 u) x (931 MeV/u) x (106eV/MeV) x (1.6 x 10 –19 J / eV) =

1.49 x 1010 J

E = mc2 so m = E/c2.

(1.49 x 1010 J) / (3x108 m/s)2 =

1.66 x 10 –27 kg

The mass units are based on the mass of a proton or 1H.

(A hydrogen nucleus)

Go to “The Nucleus” PPT

Film: Mech Univ Models of the Atom

Standard Model:Matter is composed of small subatomic particles called quarks & leptons.

Forces also have particles that transfer information through tiny particles.

See review book xerox.

Quarks

Bohr’s model could not explain why e- could occupy only certain orbits.

DeBroglie’s hypothesis for the wave nature of matter helped explain how only certain orbits were allowed.

Each e- has = h/mv.

DeBroglie proposed that each e- is a standing wave.

Proposed e- standing waves. Only ’s that fit certain orbits are possible.

’s that don’t fit circumference cannot exist.

Heisenberg’s uncertainty principle 1927.

It is impossible to be make simultaneous measurements of a particle’s position and momentum with infinite accuracy.

When you try to look to see where an e- actually is, you must give it energy. If you give it energy, it moves.

Film DeBroglie Atom

http://www.youtube.com/watch?v=IsA_oIXdF_8&feature=iv&annotation_id=annotation_40275

Alpha Rays

• A rays are helium nuclei, (2p+ and 2no), that are emitted from nucleus.

• They can be easily stopped by skin or thin sheet of paper.

• More likely to knock e- from orbits because they lose all their KE at once.

• Charge = +2e

• Mass 4 units

• Energy is KE = ½ mv2.

Beta Rays

• More penetrating than alpha.

• Less capable of ionizing because their energy is lost over greater distance.

• They are fast moving e-.

• Charge = -e.

• mass = e.

• KE = ½ mv2. v can be sig portion of c.

• Need a few mm of Al to stop them.

GammaPenetrating power greatest. Can pass thru human body, concrete, and lead.

Lowest ionizing power.

They are EM waves.

No charge. No mass.

Energy described by E = hf.

Travel with vel of light in vacuum.

No maximum stopping range.

How could we distinguish the different types of radiation? What could we observe?

Hwk rd 450 –462 Core only

Do quest pg 451 1-5p 457 1-4p 458 1-3p 462