Thurs. Nov. 19, 2009 Phy208 Lect. 23 1

Exam 3 is Thursday Dec. 3 (after Thanksgiving)

Students w / scheduled academic conflict please stay after class Tues. Nov. 24 to arrange alternate time.

5:30-7 pm, Birge 145

Covers: all material since exam 2.

Bring: Calculator

One (double-sided) 8 1/2 x 11 note sheet

Schedule:

Week14HW: assigned Thur. Nov. 19, due Fri. Dec. 4 (two weeks)

Last material for exam: Lecture of Tues. Nov. 24

Exam review: Tuesday, Dec. 1, in class

Thurs. Nov. 19, 2009 Phy208 Lect. 23 2

Summary of Photoelectric effect

Light comes in photons - particles of light h=Planck’s constant

Red photon is low frequency, low energy.

(Ultra)violet is high frequency, high energy.

Electron in metal absorbs one photon Can escape metal if photon energy large enough

Ephoton>Work function Eo

Excess energy Ephoton-Eo shows up as kinetic energy

€

E photon = hf = hc /λ

Thurs. Nov. 19, 2009 Phy208 Lect. 23 3

Photon properties of light Photon of frequency f has energy hf

Red light made of ONLY red photons The intensity of the beam can be increased by

increasing the number of photons/second. Photons/second = energy/second = power

€

E photon = hf = hc /λ

€

h = 6.626 ×10−34 J ⋅s = 4.14 ×10−15eV ⋅s

€

hc =1240eV ⋅nm

Thurs. Nov. 19, 2009 Phy208 Lect. 23 4

Quantization of light

Possible energies for green light (=500 nm)

E=hf

E=2hf

E=3hf

E=4hf

One quantum of energy:one photon

Two quanta of energytwo photons

etc

Think about light as a particle rather than wave.

Quantum mechanically, brightness can only be changed in steps, with energy differences of hf.

En

erg

y

Thurs. Nov. 19, 2009 Phy208 Lect. 23 5

Thompson’s model of atom

J.J. Thomson’s model of atom A volume of positive charge Electrons embedded throughout

the volume A change from Newton’s model

of the atom as a tiny, hard, indestructible sphere

This model is not correct!

Thurs. Nov. 19, 2009 Phy208 Lect. 23 6

Thurs. Nov. 19, 2009 Phy208 Lect. 23 7

Resulted in new model Planetary model Based on results of thin

foil experiments Positive charge is

concentrated in the center of the atom, called the nucleus

Electrons orbit the nucleus like planets orbit the sun

Thurs. Nov. 19, 2009 Phy208 Lect. 23 8

Difference between atoms Simplest is Hydrogen:

1 electron orbiting 1 proton

Other atoms number of orbiting negative electrons same as number of

positive protons in nucleus Different elements have different number of

orbiting electrons Helium: 2 electrons Copper: 29 electrons Uranium: 92 electrons! Organized into periodic table of elements

First concentrate on hydrogen atom

Thurs. Nov. 19, 2009 Phy208 Lect. 23 9

Circular motion of orbiting electrons: electrons emit EM radiation at orbital frequency.

Similar to radio waves emitted by accelerating electrons in a antenna.

In an atom, emitted EM wave carries away energy Electron predicted to continually lose energy. The electron would eventually spiral into the nucleus However most atoms are stable!

Planetary model and radiation

Thurs. Nov. 19, 2009 Phy208 Lect. 23 10

Line spectra from atoms Atoms do emit radiation,

but only at certain discrete frequencies.

Emission pattern unique to different atoms

Spectrum is an atomic ‘fingerprint’, used to identify atoms (e.g. in space).

Hydrogen

Mercury

Wavelength (nm)

Thurs. Nov. 19, 2009 Phy208 Lect. 23 11

The Bohr atom Retained ‘planetary’ picture with

circular orbits

Only certain orbits are stable

Radiation emitted only when electron jumps from one stable orbit to another.

Here, the emitted photon has an energy ofEinitial-Efinal

Stable orbit

Stable orbit

Einitial

Efinal

Photon

Thurs. Nov. 19, 2009 Phy208 Lect. 23 12

Energy levels Instead of drawing orbits, just indicate energy an

electron would have if it were in that orbit.Zero energy

n=1

n=2

n=3

n=4

€

E1 = −13.6

12 eV

€

E2 = −13.6

22 eV

€

E3 = −13.6

32 eV

En

erg

y

axis

Thurs. Nov. 19, 2009 Phy208 Lect. 23 13

Hydrogen atom energiesZero energy

n=1

n=2

n=3

n=4

€

E1 = −13.6

12 eV

€

E2 = −13.6

22 eV

€

E3 = −13.6

32 eV

En

erg

y

€

En = −13.6

n2 eV

Quantized energy levels: Each corresponds to

different Orbit radius Velocity Particle wavefunction Energy

Each described by a quantum number n

Thurs. Nov. 19, 2009 Phy208 Lect. 23 14

Emitting and absorbing light

Photon is emitted when electron drops from one quantum state to another

Zero energy

n=1

n=2

n=3

n=4

€

E1 = −13.6

12 eV

€

E2 = −13.6

22 eV

€

E3 = −13.6

32 eV

n=1

n=2

n=3

n=4

€

E1 = −13.6

12 eV

€

E2 = −13.6

22 eV

€

E3 = −13.6

32 eV

Absorbing a photon of correct energy makes electron jump to higher quantum state.

Photon absorbed hf=E2-E1

Photon emittedhf=E2-E1

Thurs. Nov. 19, 2009 Phy208 Lect. 23 15

Hydrogen emission

This says hydrogen emits only photons of a particular wavelength, frequency

Photon energy = hf, so this means a particular energy.

Conservation of energy: Energy carried away by photon is lost by the orbiting

electron.

Thurs. Nov. 19, 2009 Phy208 Lect. 23 16

Hydrogen atomAn electron drops from an -1.5 eV energy level to one with

energy of -3.4 eV. What is the wavelength of the photon emitted?

A. 827 nmB. 653 nmC. 476 nmD. 365 nmE. 243 nm

Zero energy

n=1

n=2

n=3

n=4

€

E1 = −13.6 eV

€

E2 = −3.4 eV€

E3 = −1.5 eV

Photon emittedhf=E2-E1

hf = hc/ = 1240 eV-nm/

Thurs. Nov. 19, 2009 Phy208 Lect. 23 17

Each orbit has a specific energy En=-13.6/n2

Photon emitted when electron jumps from high energy to low energy orbit.

Ei – Ef = h f Photon absorption induces

electron jump from low to high energy orbit.

Ef – Ei = h f Agrees with experiment

Energy conservation for Bohr atom

Thurs. Nov. 19, 2009 Phy208 Lect. 23 18

Hydrogen emission spectrum Hydrogen is simplest atom

One electron orbiting around one proton.

The Balmer Series of emission lines empirically given by

€

1

λm= RH

1

22−

1

n2

⎛

⎝ ⎜

⎞

⎠ ⎟

n = 3, = 656.3 nm

Hydrogen

n = 4, = 486.1 nm

n=3n=4

Thurs. Nov. 19, 2009 Phy208 Lect. 23 19

Balmer series

Transitions terminate at n=2

Each energy level has energy

En=-13.6 / n2 eV

E.g. n to 2 transition Emitted photon has energy

Emitted wavelength

€

E photon = −13.6eV

n2

⎛

⎝ ⎜

⎞

⎠ ⎟− −

13.6eV

22

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟=13.6 eV

1

22−

1

n2

⎛

⎝ ⎜

⎞

⎠ ⎟

€

λ =hc

E photon=

1240 eV − nm

13.6 eV

1

22−

1

n2

⎛

⎝ ⎜

⎞

⎠ ⎟−1

=91.18nm

1/22 −1/n2( )

Thurs. Nov. 19, 2009 Phy208 Lect. 23 20

Why stable orbits?Bohr argued that the stable orbits

are those for which the electron’s orbital angular momentum L is quantized as

€

L = me v r= n h

€

h=h

2π

⎛

⎝ ⎜

⎞

⎠ ⎟

Electron velocity

Electron orbit radius

Integer:n=1,2,3…

Bohr combined this with the Coulomb force to find allowed orbital radii and energies.

Thurs. Nov. 19, 2009 Phy208 Lect. 23 21

Including more physics

Circular orbit, electron is accelerating (centripetal acceleration = v2/r = Force/mass)

Force causing this accel. is Coulomb force ke2/r2

between pos. nucleus and neg. electron

Also gives a condition for angular momentum.

€

v 2

r =

FCoulombm

Thurs. Nov. 19, 2009 Phy208 Lect. 23 22

Bohr model of H-atom

Quantization:

Orbital motion:

€

v 2

r = FCoulomb /m = k

e2

r2/m

centripetal acceleration

Coulomb force / mass

€

L2 = mvr( )2

= n2h2€

L2 = mvr( )2

= mke2r€

p = mv

Thurs. Nov. 19, 2009 Phy208 Lect. 23 23

Radius of H-atom states

€

L2 = n2h2

€

L2 = mke2rand

Quantization Orbital motion

€

n2h2 = mke2r

r = n2 h2

mke2

⎛

⎝ ⎜

⎞

⎠ ⎟= n2ao

€

ao = Bohr radius

≈ 0.529ÅQuantized orbital radius

n orbit radius

1 ao

2 4ao

3 9ao

Thurs. Nov. 19, 2009 Phy208 Lect. 23 24

Energy of H-atom states

Total Energy = kinetic + potential

€

p2

2m

⎛

⎝ ⎜

⎞

⎠ ⎟ + −k

e2

r

⎛

⎝ ⎜

⎞

⎠ ⎟

ke2

2r

⎛

⎝ ⎜

⎞

⎠ ⎟ + −k

e2

r

⎛

⎝ ⎜

⎞

⎠ ⎟ = − k

e2

2r= −

ke2

2ao

⎛

⎝ ⎜

⎞

⎠ ⎟1

n2

€

En = −13.6 eV

n2Quantized energy

€

rn = n2ao