njit physics 320: astronomy and astrophysics – lecture v carsten denker physics department center...

NJIT

Physics 320: Astronomy and Astrophysics – Lecture V

Carsten Denker

Physics DepartmentCenter for Solar–Terrestrial Research

October 1st, 2003NJIT Center for Solar-Terrestrial Research

The Interaction of Light and MatterThe Interaction of Light and Matter

Spectral LinesSpectral LinesPhotonsPhotonsThe Bohr Model of the AtomThe Bohr Model of the AtomQuantum Mechanics and Wave–Quantum Mechanics and Wave–

Particle DualityParticle Duality


Electromagnetic Spectrum


Spectral Lines

Auguste Comte 1835 in Positive Philosophy: We see how we may determine their forms their distances, their bulk, their motions, but we can never know anything of their chemical or minerological structure.

William Wollaston, Joseph Fraunhofer, Robert Bunsen, Gustav Kirchhoff, … spectroscopy


Kirchhoff’s Laws

A hot (< 0 K), dense gas or solid object produces produces a continuous spectrum with no dark spectral lines.

A hot, diffuse gas produces bright spectral lines (emission lines).

A cool, diffuse gas in front of a source of a continuous spectrum produces dark spectral lines (absorption lines) in the continuous spectrum.


Spectroscopy

Prisms Diffraction gratings

Transmission grating Reflection grating

sin and 1, 2, 3, ...d n n

nN

nN

Resolving power


Photoelectric Effect

photon

hcE h

max photon

hcK E h


Compton Effect

photon

hcE h pc

1 cosf ie

h

m c

In a collision between a photon and an electron initially at rest, both the (relativistic) momentum and energy are conserved.

0.0243 Åce

h

m c

Compton wavelength


The Bohr Model of the Atom

Wave–particle duality of lightRutherford 1911 Au: It was quite

the most incredible event that ever happened to me in my life. It was almost as incredible as if you fired a 15–inch shell at a piece of tissue paper and it came back an hit you. discovery of a minute, massive, positively charged atomic nucleus

Proton: mp = 1836 me


Group AssignmentProblem 5.7

Verify that the units of Planck’s constant are the units of angular momentum!

2

2

-1 2

m m kg m = kg

s s

J m m = Js = Nm s = kg m s = kg

s s s

L mvr

EE h h


Hydrogen Atom1

2

1 1 1 and 109677.585 0.008 cm

4H HR Rn

2 2

1 1 1 and HR m n

m n

m = 1 UV [122, 103, 97, …] nm Lyman

m = 2 Visible [656, 486, 434, …] nm Balmer

m = 3 IR [1875, 1282, 1094, …] nm Paschen

m = 4 IR [4051, 2625, 2165, …] nm Brackett

m = 5 IR [7458, 4652, …] nm Pfundt

Planetary model of the hydrogen atom?


Bohr’s Postulates

Only orbits are stable, where the angular momentum of the electron is quantized L = nh/2=nħ, and will not radiate in spite of the electron’s acceleration.

Every allowed orbit corresponds to a distinct energy level and the transition from a distant orbit to an orbit closer to the nucleus Ephoton = Ehigh – Elow results in the emission of an energy quantum, i. e., a photon.


Bohr Atom1 2

30

1

4E

q qF r

r

Coloumb’s law

( )(1836 )0.9994556

1836e p e e

ee p e e

m m m mm

m m m m

Reduced mass

1836 1837e p e e eM m m m m m Total mass

and p eM m m

2 2 21 2

3 2 20 0

1 1

4 4

q q v e vF a r r

r r r r


2

0

12

8

eE K U K K K

r

2 22

0 0

1 1 1 and 2

2 8 4

e eK v U K

r r

h and =

2L vr n

Quantization of

angular momentum

2 222

2 20

1 1 1 1

8 2 2 2

vr neK v

r r r

22 2 11

0 0 024 and 5.29 10 m 0.529 Ånr n a n a

e


Bohr Atom (cont.)

2 4

2 2 20

1 1 113.6 eV

8 2nn

e eE

r n n

1 1 0

2 1 2 0

13.6 eV 0.529 Å

/ 4 3.40 eV 4 2.12 Å

E r a

E E r a

4 4

photon high low 2 2 2 2high low

1 1

2 2

hc e eE E E

n n

4 4

3 2 2 2 2 3high low high low

1 1 1 1 1 and

4 4H H

e eR R

c n n n n c

2 2

1 1( 13.6 eV) 1.89 eV 6565 Å

3 2HH

hcE

E


Kirchhoff’s Laws Revisited

A hot, dense gas or hot solid object produces a continuous spectrum with no dark spectral lines. This is the continuous spectrum of black body radiation, described by the Planck functions B(T) and B(T), emitted at any temperature above absolute zero. The wavelength max at which the Planck function B(T) obtains its maximum is given by Wien’s displacement law.


Kirchhoff’s Laws Revisited (cont.) A hot, diffuse gas produces bright emission lines. Emission lines

are produced when an electron makes a downward transition from a higher to a lower orbit. The energy lost by the electron is carried away by the photon.

A cool, diffuse gas in front of a source of continuous spectrum produces dark absorption lines in the continuous spectrum. Absorption lines are produced when an electron makes a transition from a lower to a higher orbit. If the incident photon in the continuous spectrum has exactly the right amount of energy, equal to the difference in energy between a higher orbit and the electron’s initial orbit, the photon is absorbed by the atom and the electron makes an upward transition to the higher orbit.


Quantum Mechanics and Wave–Particle Duality

E

h De Broglie frequency

h

p De Broglie

wavelength

1

2 or 1

2

x p x p

E tE t

Heisenberg’s uncertainty principle


Problem 4.5

2

moving2

moving

rest moving

moving rest

rest moving

10.8 1 0.6 and 60 m

( ) / 0.8 0.25 μs

60 m( ) 100 m

0.61

( ) 0.6 60 m 36 m

( ) 100 m/0.8c 0.417 μs

( ) 100 m 36 m 64 m

64 m / 0.8

P

T

T

u uL

c c

a t L c

b L L

c L L

d t

e L L

t c

0.267 μs


Problem 4.13

2

2

0.8 and 0.6 (Frame of reference @ rest = Earth)

(Eqn. 4.40)1 /

0.6 0.8= 0.946

1 (0.8 )( 0.6 ) /

0.946

A B

BB

B

A

v u c v c

v uv

uv c

c cc

c c c

v c


Problem 4.18

2

2 2 2

2 22 2 4 2 2 2 2 2 2

2 2 2 2 2

2 2

(Eqn. 4.46)

( )

(Eqn. 4.48) (1 ) (1 ) (1 )

if (1 ) 2

E mc

E mc

E m c mc mc mc mc mc mc

p c mc mc Kmc

p pK K v c

m m


Homework Class Project

Prepare a 200 – 250 word abstract for one of the five topics mentioned in the storyline

Important scientific factsForm of presentationLearning goalsHomework is due Wednesday

October 8th, 2003 at the beginning of the lecture!

Exhibition name competition!


Homework

Homework is due Wednesday October 8th, 2003 at the beginning of the lecture!

Homework assignment: Problems 5.4, 5.5, and 5.15

Late homework receives only half the credit!

The homework is group homework!Homework should be handed in as a

text document!

njit physics 320: astronomy and astrophysics – lecture v carsten denker physics department center...

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