1M_06_HEmission

Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum : 

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 : 

#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

Electromagnetic Radiation : 

Electromagnetic Radiation Oscillating electric and magnetic fields

Light Energy : 

Light Energy Wavelength l distance peak-to-peak Frequency n oscillations per second Energy E  n faster oscillation = more E

Electromagnetic Spectrum : 

Electromagnetic Spectrum

Visible Emission : 

Visible Emission Wavelengths, l, increase Energies decrease Electronic transitions (“e- jumps”) 400 nm 500 nm 600 nm 700 nm

Dual Nature of Light/Relationships : 

Dual Nature of Light/Relationships h Planck’s constant = 6.626×10-34 J.s Units J = (J.s) (s-1) c speed of light = 2.998×108 m.s-1 Units s-1 = (m.s-1)/(m) 1. Wave wavelength, l frequency, n 2. Particle photon = “packet” E = hn

Using the Equations : 

Using the Equations (a) Calculate the frequency of 460nm blue light. (b) Calculate the energy of 460 nm blue light.

Spectroscopy : 

Spectroscopy Spectroscopy: study of interaction of light with matter hn: photon 1. Absorption: matter + hn → matter* 2. Emission: matter* → matter + hn Energy change in matter: DEmatter = Ehn

Discrete Energy Levels : 

Discrete Energy Levels Observed energy level changes: DE = Ehn = Efinal – Einitial Ground state atom Absorption Emission

“Discrete” Atomic Emission : 

“Discrete” Atomic Emission Atomic absorption: electrons excited to higher energy levels Atomic emission: excited electrons lose energy Incandescent Hot Gas Cold Gas Continuous Discrete Emission Discrete Absorption

Quantized Energy Levels : 

Quantized Energy Levels Ehn = DElevels DE = Ef – Ei Absorption: Ef > Ei Emission: Ef < Ei

Hydrogen Emission Spectrum : 

Hydrogen Emission Spectrum ©The McGraw-Hill Companies. Permission required for reproduction or display

H atom emission : 

H atom emission 1) Electrical energy excites H H + energy  H* initial quantum state ni = 2, 3, 4, 5, 6, … 2) H* loses energy H*  H + hn final quantum state nf = 1, 2, 3, … nf < ni You observe several DEtransitions  visible ls ni’s levels > nf nf end at same nf You determine ni’s and nf

Hydrogen Atom and Emission : 

Hydrogen Atom and Emission n = 1 n = 2 n = 3 n = 4 n = ...infinity Lyman Balmer Paschen Ground State: n = 1 Excited States: n = 2, 3, 4, …

Rydberg Equation : 

Rydberg Equation A “series” is associated with two quantum numbers: Lyman: ni = 2, 3, 4, … nf = 1 Balmer: ni = 3, 4, 5, … nf = 2 Paschen: ni = 4, 5, 6, … nf = 3 RH = 1.096776×107m-1 = 2.180×10-18 J = 2pe4m/h3c General transition eq’n: Hydrogen atomic emission lines fit (Rydberg eq’n):

Hydrogen Atomic Emission : 

Increasing l (decreasing E, smaller DE) n = principal E states (principal quantum #s) Hydrogen Atomic Emission Energy

Part 1 Correlate color with wavelength : 

Part 1 Correlate color with wavelength Use lucite rod 20 nm intervals, 400–700 nm l, color Boundary ls lshort, llong l of max. intensity lmax Observe Hg atomic emission (handheld specs)

Part 2 Calibrate Spectrometer : 

Part 2 Calibrate Spectrometer Determine if measured wavelengths are “true” Use He emission Record lmsr for lines Plot ltrue vs lmsr 7 or 8 lines

Calibration Plot : 

Calibration Plot H atom emission: Multiply: lmsrd by slope Converts: measured ltrue l

Part 3 Record H emission ls : 

Part 3 Record H emission ls Record color, lmsr (3 or 4 lines) color, lmsr Determine ltrue ltrue Calculate Ehn from ltrue Ehn Units: E in J h in J.s c in m/s l in m

Questions/Data Analysis : 

Questions/Data Analysis 1) Which set of lines? Balmer or Paschen (nfinal = ?) 2) What is ninitial for each line? 3) What is your experimental RH?

Hydrogen Lines / Analysis : 

Hydrogen Lines / Analysis

One way to think about the data : 

One way to think about the data Which series are we observing – Balmer or Paschen? Balmer: nf = 2 32, 42, 52 Paschen: nf = 3 43, 53, 63 These would be the three lowest energy transitions Example data:

Compare calculated ΔE to observed ΔE : 

Compare calculated ΔE to observed ΔE EH atom  1/n2 = RH/n2 so calculate En=1, En=2, etc. Find ΔE between levels and compare to observed E’s Experiment matches Balmer best

How? Plot DEatom vs. 1/ni2 : 

How? Plot DEatom vs. 1/ni2 Rearranged Rydberg equation fits:

Example Balmer Rydberg Plot : 

Example Balmer Rydberg Plot Slope (~RH): 2×10-18J Close to RH 2.18×10-18J x-intercept: ~0.24 Close to 0.25 ~1/22

Balmer (nf = 2) – plot ΔE vs. 1/ni2 : 

Balmer (nf = 2) – plot ΔE vs. 1/ni2 Good: Slope  –RH x-intercept: 1 22 so nf = 2 ~ 0.25 = This plot verifies our data – we observed the Balmer series!

An alternative way to analyze the data : 

An alternative way to analyze the data 1) Data is for: Balmer (nf = 2) or Paschen (nf = 3) Be sure to correct wavelengths (measured  true) 2) Transitions are 3 lowest energy: Balmer (ni = 5, 4, 3) or Paschen (ni = 6, 5, 4)

Graphs : 

Graphs Prepare two graphs (Balmer and Paschen) x-axis should extend to x-intercept (y = 0) y-axis should be appropriate Draw best-fit straight line Find slope (one should be close to –RH) Find relative error in experimental RH Match l and color to ni and nf

Paschen (nf = 3) : 

Paschen (nf = 3) Not too good Slope ≠ RH x-int. ≠ 1/32

Balmer (nf = 2) : 

Balmer (nf = 2) Good: Slope  –RH x-intercept: 1 22 so nf = 2 ~ 0.25 =

Example Balmer Rydberg Plot : 

Example Balmer Rydberg Plot Slope (~RH): 2×10-18J Close to RH 2.18×10-18J x-intercept: ~0.24 Close to 0.25 ~1/22

Data : 

Data Experimental RH: 2 ×10-18 J

1/l vs. 1/ni2 : 

1/l vs. 1/ni2

Report : 

Report Abstract Results 2a: Calibration data and plot 2b: Table Series plot (or Balmer and Paschen plots) depending on your analysis choice RH and error from literature Predicted wavelengths and error Sample calculations of: photon energy and Rydberg slope Discussion/review questions