Announcements

• Reading next class 5.7

• Homework 6 due Wednesday.

• Exam 2 next week (Thursday)

– Inclusive there will be some SR.

– Modern physics

– Photons and PE

– Atomic spectra

– Bohr atom etc.

Atoms/ Balmer/ Bohr atom

A neon lamp emits a red line. Sodium emits a yellow line.

What accounts for this difference?

a.The electrons in the discharge lamp hit the neon atoms

with higher kinetic energy than the electrons hit the sodium

atoms

b.The electrons in the discharge lamp hit the neon atoms

with less speed than the electrons hit the sodium atoms

c.The energy spacing between the electronic energy levels

that are responsible for these lines are smaller in the neon

atom than in the sodium atom.

d.The energy spacing between the electronic energy levels

that are responsible for these lines is larger in the neon

atom than in the sodium atom.

What we know so far about atoms:

n

n

n p

p

p

p n

n n

n p Rutherford: Atoms have a tiny, but very dense

core surrounded by a cloud of electrons.

120V

Discharge lamps: Atoms struck by fast

electrons emit light of distinct colors.

Energy levels: Electrons in atoms are found only

in discrete energy levels. When they jump

down to a lower level, a photon is emitted

carrying away the energy.

Different Atoms: Different types of atoms have different level

structures (seen by the distinct set of colors they emit):

Neon: Strong red line; Sodium: strong yellow line …

e

ΔE ΔE=hf

a. arrows on right represent absorption of light,

arrows on left represent emission.

b. arrows on both left and right represent emission

c. arrows on both left and right represent absorption

d. arrows on left represent absorption of light,

arrows on right represent emission.

e. I don’t know. I have never seen such a diagram.

incre

asin

g

energ

y allowed energies in an atom

“ground state”

What do the vertical arrows represent?

increasing

energy

allowed energies

ground state

d. arrows on left represent absorption of light,

arrows on right represent emission.

e

e

e e

e

e

For Hydrogen, transitions to ground state in deep ultraviolet!

No light emitted with

colors in this region

because no energy

levels spaced with

this energy.

Energy level diagrams represent energy levels the electron can

go to. Different height = different energy

En

erg

y

An single electron bashes into an atom in a discharge lamp

10 V

If atom fixed at the center of the tube,

list all the possible photon energies (colors) that you might see?

A. 1eV, 2eV, 3eV, 4eV, 7eV, 8eV

B. 4eV, 7eV, 8eV

C. 1eV, 3eV, 4eV

D. 4eV

E. Impossible to tell.

-10eV

-6 eV

-3 eV

-2 eV + -

Electron leaves hot filament with

nearly zero initial kinetic energy

An single electron bashes into an atom in a

discharge lamp

10 V

If atom fixed at this point in tube,

list all the possible photon energies (colors) that you might see?

A. 1eV, 2eV, 3eV, 4eV, 7eV, 8eV

B. 4eV, 7eV, 8eV

C. 1eV, 3eV, 4eV

D. 4eV

E. Impossible to tell.

-10eV

-6 eV

-3 eV

-2 eV

Answer is D. Electron only gains about 5eV!

Electron energy = qV = e(Ed),

where E is the electric field = (battery V)/(total distance D),

and d is the distance it goes before a collision.

D d

+ -

When an emission line appears very bright that

means:

a.Multiple photons are emitted for each single

electron transition

b.More electron transitions are occurring each

second

c.The electronic energy levels are farther apart

and thus the line appears brighter

d.a and b

e.b and c Why do I have a problem with this question?

When an emission line appears very bright (to

an intelligent observer) that means:

a.Multiple photons are emitted for each single

electron transition

b.More electron transitions are occurring each

second

c.The electronic energy levels are farther apart

and thus the line appears brighter

d.a and b

e.b and c

Answer is b. Each electron transition produces

exactly one photon with energy equal to energy

difference between electron energy levels. More

electron transitions, more photons, brighter line.

But this assumes we’ve corrected for what

“apparent” brightness is.

Applications of atomic spectroscopy 1. Detecting what kind of atoms are in a material.

(excite by putting in discharge lamp or heating in flame

to see spectral lines)

telescope

diffraction

grating

star

3. Making much more efficient lights!

Incandescent light bulbs waste >90% of the electrical

energy that goes into them! (<10% efficient)

Streetlight discharge lamps (Na or Hg) ~80%

efficient. Fluorescent lights ~ 40-60% efficent.

2. Detecting what the sun and the stars are made of:

Look at the light from a star through a diffraction grating.

See what lines there are; Match up to atoms on earth.

Let’s investigate the internal

working of a galaxy

Atomic spectra in astronomy

L

R

L

R

longer wavelength

lower frequency

Spectral lines from

atoms in stars

Hubble and the big bang

Edwin Hubble, PNAS March 15, 1929 vol. 15 no. 3 168-173

Spectral lines from Hydrogen

Application:

Designing a better light

What is important?

(Well, we have to be able to see the light!)

What color(s) do you want?

(red, green & blue is what our eyes can see)

How do you excite the atoms to desired level?

( Electron collisions)

How to get electrons with desired energy when

hit atoms? What determines energy of electrons?

Hot electrons jump

between many very

closely spaced levels

(solid metal). Produce all

colors. Mostly infrared at

temp of normal filament.

>90% is worthless

Infrared radiation (IR =

longer than ~700nm)

Incandescent light (hot filament)

Temperature = 2500-3000K

λ

IR

~10% of energy is

useful visible light

P Right atom, right pressure

and voltage, mostly visible light.

Streetlight discharge lamps

(Na or Hg) 80% efficient.

Energy levels in

isolated atom:

Only certain

wavelengths

emitted.

Discharge lamp

HV

Converting UV light into visible photons with “phosphor”.

Phosphor converts 180 nm UV to red+ green+blue.

Florescent Lights. Discharge lamp, but want to have it look white.

White = red + green +blue

40-60% efficient (electrical power ⇒ visible light)

phosphor wastes 20-30% energy ⇒ heat

How to do this?

180nm 6.9 eV energy per photon

633nm (red) 2 eV / photon

532nm (green) 2.3 eV / photon

475nm (blue) 2.6 eV / photon } 6.9 eV

Hg

180 nm far UV

phosphor

coating

energy of electron

in phosphor molecule

Converting 180nm UV light into visible photons with “phosphor”.

Florescent Lights. Discharge lamp, White= Red + green +blue

40-60% efficient (electrical power⇒visible light)

e

Hg

Hg

Hg

Hg

discharge lamp/flor. tube

120 V

phosphor wastes 20-30% energy

⇒ heat

real phosphors more than just 3

Hg

Summary of important Ideas

Hydrogen

Energ

y

Lithium

Electron energy levels in 2

different atoms: Levels have

different spacing (explains

unique colors for each type of

atom.

Atoms with more than one

electron … lower levels filled. (not to scale)

1) Electrons in atoms are found at specific energy levels

2) Different set of energy levels for different atoms

3) one photon emitted per electron jump down between energy

levels. Photon color determined by energy difference.

4) If electron not bound to an atom: Can have any energy. (For

instance free electrons in the PE effect.)

Now we know about the energy

levels in atoms. But how can we

calculate/predict them?

Step 1: Make precise, quantitative observations!

Step 2: Be creative & come up with a model.

Step 3: Put your model to the test.

Need a model

Balmer series:

A closer look at the

spectrum of hydrogen

As n gets larger, what happens to wavelengths of

emitted light?

λ gets smaller and smaller, but it approaches a limit.

656.3 nm 486.1 434.0

410.3

Balmer (1885) noticed wavelengths followed a progression

22

1

2

1

nm19.91

n

where n = 3,4,5, 6, ….

22

1

2

1

nm19.91

n

where n = 3,4,5,6, ….

λ gets smaller and smaller, but it approaches a limit

gets smaller as n increase

gets larger as n increase,

but no larger than 1/4

364.7nmnm19.91*4limit

Balmer correctly

predicted yet

undiscovered

spectral lines.

So this gets smaller

Balmer series:

A closer look at the

spectrum of hydrogen

656.3 nm 486.1 410.3

Balmer (1885) noticed wavelengths followed a progression

434.0

Hydrogen atom – Rydberg formula Does generalizing Balmer’s formula work?

Yes! It correctly predicts additional lines in HYDROGEN.

22

11

nm19.91

nm

Rydberg’s general formula Hydrogen energy levels

n

m (m=1,2,3..)

(n>m)

Predicts of nm transition:

m2

m=1, n=2

Hydrogen atom – Lyman Series

m=1

Hydrogen

energy

levels 0eV

-?? eV

Can Rydberg’s formula

tell us what ground

state energy is?

22

11

nm19.91

nm

Rydberg’s formula

n

m (m=1,2,3..)

(n>m)

Predicts of nm transition:

22

11

nm19.91

nm

Balmer-Rydberg formula Hydrogen energy levels

0eV

-?? eV

Look at energy for a transition between n=infinity and m=1

22

11

19.91 nmnm

hchcEE finalinitial

0eV 0

2

1

19.91 mnm

hcE final

2

16.13

meVEm

22

11

nm19.91

nm

where m=1,2,3 and where n = m+1, m+2

Balmer’s formula

m=1, n=2

Hydrogen energy levels

656.3 nm 486.1

434.0

410.3

Balmer/Rydberg had a mathematical formula to describe

hydrogen spectrum, but no mechanism for why it worked!

Why does it work?

The Balmer/Rydberg formula is a

mathematical representation of an

empirical observation.

It doesn’t explain anything, really.

How can we calculate the energy levels

in the hydrogen atom?

A semi-classical explanation of the

atomic spectra (Bohr model)