Atomic spectrum and atomic shell model( 原子からの光のスペクトラムと原子の量子状態 )

柴田研究室　　07M01165 田森 緑

H

1. Atomic shell model

He r12

+2e

-e-e

r1

r2

with variational method (変分法)

Effective charge of nucleus : Coulomb shielding

1.69

2. Experiment

diffraction lattice(回折格子)

digitalcamera

spectroscope

spectral lamp

0

5 cm

experimental set up

virtual image

continuous spectrum of white lamp

Diffraction lattice can separate light of different wavelength.

take a photo with digital camera and transfer it to a PC

diffraction lattice spectroscope

at Tamarokuto science museum, November 2006

example

4. Analysis

spectral lamp

Hydrogen gas or helium gas are sealed into a glass tube.

A high voltage of 25kV is supplied.

1) emitted electrons hit directly atom.2) Bound electrons are excited.3) fall into the lower state4) photon is emitted.

spectrum of H

calibration of position against wavelength

slit 47.351. blue 587.772. light blue 651.703. red 876.46

position (pixel)spectral lineExperimental results transition wavelength

5 2 434 nm→4 2 486 nm→3 2 656 nm→

n energy (eV)

1 -13.598 2 -3.4003 -1.5114 -0.8505 -0.5946 -0.388

expected energy

H

Fit with a straight line,

Linearity is good between position and wavelength.

0.766 ± 0.00521.2 ± 3.1

histogram of spectrum and strength of peaks

spectral line position (pixel) wavelength (nm) transition

1 714.3 442 4d 2p→2 743.1 464 4s 2p→3 769.6 484 4d 2p→4 781.7 493 3p 2s→5 890.0 577 3d 2p→6 994.7 657 3d 2p→

experimental

Wavelengths of six lines are determined.

=

with calibrationusing hydrogen lines

0.766 ± 0.00521.2 ± 3.1

transitionprobability ( /s)

wavelength (nm)

1.2.3.

Integrate the peaks

spectral line integral

1 0.132 3.963 0.91

H

branching ratioBranching ratio can be calculated with transition probability.

I will calibrate detection efficiency.

After the calibration,information on population of initial states can be studied from strength of peak of histogram.

5 4

1

2

3

n

100 % 65 % 55 % 49 %

35 % 25 % 22 %

15 %

14 %

20 %

visible

Balmer series

-13.6

-1.41

-3.40

0

V(r) ( eV ) r A1 2 3 4

V r =−e2

r

Lyman

Balmer

Paschen

n=1

n=2

n=3

interference

parallellight

diffraction lattice

spectrum of He

3. Results

Shell model is a basic concept in quantum mechanics.

- atomic shell model - nuclear shell model　・・・ shell structure of nucleons - quark shell model 　・・・ shell structure of quarks in hadron

I analyzed atomic spectrum to study atomic shell model.

slit

1 2 3 pixel

5. Summary and Outlook ・Shell model is a basic concept of bound particles in quantum mechanics. ・It is important to study atomic shell model. ・Lines from atoms were measured with spectroscope using diffraction lattice. ・Three lines in hydrogen, six lines in helium are observed : Balmer series ・I took a photo with digital camera and transfered it into a PC. ・I analyzed. - calibration of position against wavelength - wavelengths of six lines in helium are determined - histogram of spectrum - branching ratio ・After the calibration of detection efficiency, information on population of initial states will be studied.

H

He