emission series and emitting quantum states visible h
play

Emission Series and Emitting Quantum States: Visible H Atom - PDF document

Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum Experiment 6 #6 Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum Goal: To determine information regarding the quantum states of the


  1. Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum Experiment 6 #6 Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum Goal: � To determine information regarding the quantum states of the H atom Method: � Calibrate a spectrometer using He emission lines � Observe the visible emission lines of H atoms � Determine the initial and final quantum states responsible for the visible emission spectrum, as well as the Rydberg constant 1

  2. Electromagnetic Radiation ���������������������������������������� Light Energy � ���������� ��������������������� λ λ λ λ � ������������ ����������������������� ν ν ν ν � ������ �� ∝ ���������������������������� ∝ ν ν ∝ ∝ ν ν 2

  3. Electromagnetic Spectrum Visible Emission 400 nm 500 nm 600 nm 700 nm ������������� λ ����������� ����������������� �������������������������� � ����!" 3

  4. Dual Nature of Light/Relationships wavelength, λ 1. Wave frequency, ν 2. Particle photon = “packet” E = h ν Planck’s constant = 6.626×10 -34 J . s h h � E = J = (J . s) (s -1 ) Units c c speed of light = 2.998×10 8 m . s -1 � = s -1 = (m . s -1 )/(m) � Units Using the Equations (a) Calculate the frequency of 460nm blue light. m 8 × ( 2 . 99 10 ) c s ν = λ = � � 1 m � � (460 nm) � � 9 × 1 10 nm 14 - 1 = × 6 . 52 10 s (b) Calculate the energy of 460 nm blue light. hc E = = h ν λ - 34 14 − 1 = × ⋅ × (6.626 10 J s )( 6.52 10 s ) - 19 = 4 . 32 × 10 J 4

  5. Spectroscopy Spectroscopy: study of interaction of light with matter h ν # ������ matter + h ν � matter* 1. Absorption: � matter + h ν 2. Emission: matter* �����������������������# ∆ ∆ E matter = E h ν ∆ ∆ ν ν ν Discrete Energy Levels Ground state atom Absorption Emission �$���������������������������# ∆ �������� � ν ����� ����� � � ������� 5

  6. “Discrete” Atomic Emission Incandescent Continuous Hot Gas Discrete Emission Cold Gas Discrete Absorption %�������$��������# �����������&����������������������������� %��������������# �&��������������������������� Quantized Energy Levels � � ν �� ∆ � ������ ∆ ����� � � � � %$��������#��� � '�� � ��������#������ � (�� � 6

  7. Hydrogen Emission Spectrum )*���+�,��-�.����/��������0�1���������������������������������������������� H atom emission 2" �������������������&������. ���������� → �� → → → ���������������������� � � ������������������ � 3" .4������������� ��� ����� ν → → → → ν ν ν ������������������� � � ������������ � � � � � � 5����$�������������� ∆ � ����������� ≡ ����$��� λ � � � 6� �������'�� � � 5�������������� � 6� ����� � � � ������������� � � 7

  8. Hydrogen Atom and Emission ������������� ����2 � !����������"� Balmer ����3��7��8��9 Lyman Paschen Rydberg Equation � E = − = General transition eq’n: E E E h � f i levels � � Hydrogen atomic 1 1 � � = − E R emission lines fit � � h � H 2 2 n n � � ( Rydberg eq’n ): f i � � ���������� ×10 7 � �� ����������� ��� �� = 2 π e 4 m/h 3 c A “series” is associated with two quantum numbers: Lyman: n i = 2, 3, 4, … n f = 1 Balmer: n i = 3, 4, 5, … n f = 2 Paschen: n i = 4, 5, 6, … n f = 3 8

  9. Hydrogen Atomic Emission ������ → � ��������������������� ∆ �' �������������������:�" $��!���"�������"%�&&��� ∆ ∆ ∆ � � #�!���"��� λ λ λ λ 1 1 � � � � = − � � �� � � � 2 2 � � � � Part 1 Correlate color with wavelength Use lucite rod � λ λ , color 20 nm intervals, 400–700 nm λ λ � Boundary λ s λ short , λ λ λ long λ λ λ λ � λ of max. intensity λ max λ λ λ � Observe Hg atomic emission (handheld specs) 9

  10. Part 2 Calibrate Spectrometer Determine if measured wavelengths are “true” Accepted Measured λ λ λ λ � Use He emission Color λ λ λ (nm) λ (nm) � Record λ λ msr for lines λ λ red 728.1 730 � Plot λ λ true vs λ λ msr λ λ λ λ red 706.5 710 red 667.8 670 � 7 or 8 lines yellow 587.5 590 green 501.5 500 green 492.2 490 blue-green 471.3 470 blue-violet 447.1 450 Calibration Plot 728.1 720 730 706.5 ����20;;32& y − y 710 2 1 = slope < 3 ���;0===> 680 667.8 − x x 670 2 1 640 ∆ λ true = ∆ λ True (nm) 600 msrd 587.5 590 560 H atom emission: 501.5 520 •Multiply: 500 λ msrd by slope 492.2 447.1 480 •Converts: 490 450 471.3 measured λ→ true λ 470 440 440 480 520 560 600 640 680 720 Measured λ (nm) 10

  11. Part 3 Record H emission λ s − e * *  → → → + ν H H 2 H 2 H h 2 ( g ) 2 ( g ) ( g ) ( g ) ( lines ) * → + ν H H h 2 ( g ) 2 ( g ) ( bands ) color, λ λ msr λ λ � Record color, λ λ λ λ msr (3 or 4 lines) λ λ λ λ true � Determine λ λ λ true λ E h ν ν from λ λ true λ λ � Calculate E h ν ν ν ν ν ν Units: E in J hc E h � = h in J . s � c in m/s λ in m Questions/Data Analysis 1) Does your data match the Balmer series (it should; n final = 2? ) 2) What is n initial for each line? What is your experimental R H ? 3) 11

  12. Hydrogen Lines / Analysis Color λ (nm) ∆ E (J) red 660 3.0×10 -19 4.1×10 -19 blue-green 490 4.6×10 -19 blue-violet 430 4.8×10 -19 violet 410 � � 1 1 � � � E = − = E R � � h � H atom 2 2 n n � � f i One way to think about the data %���-���$������������?����� ��������������������@ ?�����# � � ��3 7 → 3��8 → 3��A → 3 *�����-�����$��������������-���������������������� �&����������# B��������� �$������ λ (nm) λ (nm) ∆ E (J) Color 82;02 ������ 8;; A0;��2= 8780; $���������� 87; 80>��2= 8C>02 $��������� A;; 80;��2= >A>03 ��� >A; 702��2= 12

  13. Compare calculated � E to observed � E E H atom ∝ 1/n 2 = R H /n 2 so calculate � E between levels and compare to observed E’s Theoretical Observed % λ (nm) Color ∆ E (J) λ (nm) Color ∆ E (J) error 82;02 ������ 80C8��2= 8;; ������ A0;��2= 2.6 8780; $���������� 80AC��2= 87; $���������� 80>��2= 1.0 8C>02 $��������� 80;=��2= A;; $��������� 80;��2= 2.7 >A>03 ��� 70;7��2= >A; ��� 702��2= 1.0 Experiment matches Balmer well (<5% error) 2 How? Plot ∆ ∆ E atom vs . 1/n i ∆ ∆ Rearranged Rydberg equation fits: = + y m x b � � 1 R � � � E H = − + R � � atom H 2 2 � � n n i f R H y − intercept = = − slope R 2 H n f � E − = x intercept : 0 1 1 so : = 2 2 n n f i 13

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend


More recommend