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

Transcription

1 Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum Experiment 6 Goal: #6 Emission Series and Emitting Quantum States: Visible H Atom Emission Spectrum 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 Oscillating electric and magnetic fields Light Energy Wavelength λ distance peak-to-peak Frequency ν oscillations per second Energy E ν faster oscillation = more E

3 Electromagnetic Spectrum Visible Emission 400 nm 500 nm 600 nm 700 nm Wavelengths, λ, increase Energies decrease Electronic transitions ( e - jumps ) 3

4 Dual Nature of Light/Relationships 1. Wave wavelength, λ frequency, ν. Particle photon = packet E = hν h Planck s constant = J. s Units J = (J. s) (s -1 ) E = hν c speed of light = m. s -1 Units s -1 = (m. s -1 )/(m) ν = c λ (a) (b) Using the Equations Calculate the frequency of 460nm blue light. 8 m ( ) c ν = = s λ 1 m (460 nm) nm = Calculate the energy of 460 nm blue light. hc E = = hν λ = ( = J 14 s -1 J s)( s 1 ) 4

5 Spectroscopy Spectroscopy: hν: study of interaction of light with matter photon 1. Absorption: matter + hν matter*. Emission: matter* matter + hν Energy change in matter: E matter = E hν Discrete Energy Levels Ground state atom Absorption Emission Observed energy level changes: E = E hν = E final E initial 5

6 Incandescent Discrete Atomic Emission Continuous Hot Gas Discrete Emission Cold Gas Discrete Absorption Atomic absorption: electrons excited to higher energy levels Atomic emission: excited electrons lose energy Quantized Energy Levels E hν = E levels E = E f E i Absorption: E f > E i Emission: E f < E i 6

7 Hydrogen Emission Spectrum The McGraw-Hill Companies. Permission required for reproduction or display H atom emission 1) Electrical energy excites H H + energy H* initial quantum state n i =, 3, 4, 5, 6, ) H* loses energy H* H + hν final quantum state n f = 1,, 3, n f < n i You observe several E transitions visible λs n i s levels > n f n f end at same n f You determine n i s and n f 7

8 Ground State: n = 1 Hydrogen Atom and Emission Excited States: n =, 3, 4, Lyman Balmer Paschen General transition eq n: Rydberg Equation E = E E = hν f i E levels Hydrogen atomic emission lines fit (Rydberg eq n): E hυ 1 1 = RH n f ni R H = m -1 = J = πe 4 m/h 3 c A series is associated with two quantum numbers: Lyman: n i =, 3, 4, n f = 1 Balmer: n i = 3, 4, 5, n f = Paschen: n i = 4, 5, 6, n f = 3 8

9 Hydrogen Atomic Emission Energy n = principal E states (principal quantum #s) E 1 1 n f ni hυ = RH Increasing λ (decreasing E, smaller E) Part 1 Correlate color with wavelength Use lucite rod 0 nm intervals, nm λ, color Boundary λs λ short, λ long λ of max. intensity λ max Observe Hg atomic emission (handheld specs) 9

10 Part Calibrate Spectrometer Determine if measured wavelengths are true Use He emission Record λ msr for lines Plot λ true vs λ msr 7 or 8 lines Accepted Measured λ Color λ (nm) (nm) red red red yellow green green blue-green blue-violet Calibration Plot slope = y x λ = λ y1 x true msrd H atom emission: Multiply: λ msrd by slope Converts: measured λ true λ 1 True (nm) y = 1.001x R = Measured λ (nm) 10

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

12 Hydrogen Lines / Analysis Color red blue-green blue-violet violet λ (nm) E (J) E hυ R 1 1 = H = n f n i E atom One way to think about the data Are we observing the Balmer series, as predicted? Balmer: n f = 3, 4, 5 These would be the three lowest energy transitions Example data: Literature Observed λ (nm) Color λ (nm) E (J) violet E blue-violet E blue-green E red E-19 1

13 Compare calculated E to observed E E H atom 1/n = R H /n so calculate E between levels and compare to observed E s Theoretical Observed % λ (nm) Color E (J) λ (nm) Color E (J) error violet 4.84E violet 5.0E blue-violet 4.58E blue-violet 4.6E blue-green 4.09E blue-green 4.0E red 3.03E red 3.1E Experiment matches Balmer well (<5% error) How? Plot E atom vs. 1/n i Rearranged Rydberg equation fits: y E atom = slope = R H m = R H x 1 n i + + b R n H f y intercept = R n H f x intercept : so : E = = n f n i 13

14 Example plot data y = m x + b E atom = R H 1 n i + R n H f Corrected λ Balmer color nm E f -E i (J) n i n f 1/n i red E blue-green E blue-violet E violet E y-axis x-axis Example Balmer Rydberg Plot Slope (~R H ): J Close to R H J Ef-Ei 6.0E E E E-19 Balmer Series y = -x10-18 x + 6x10-19 R = x-intercept: ~0.4 Close to 0.5 ~1/.0E E E+00 λ (nm) Color λ (nm) E (J) violet E blue-violet E blue-green E red E /n 14

15 Balmer (n f = ) plot E vs. 1/n i 5.0E E-19 y = -x10-18 x + 5x10-19 R = Good: Slope R H 3.0E-19 E.0E E E /n i x-intercept: ~ 0.5 = so n f = 1 This plot verifies our data we observed the Balmer series! 1) Data for: As an extension (extra) Balmer (n f = ) or Paschen (n f = 3) ) Transitions are 3 lowest energy: Balmer (n i = 5, 4, 3) or Paschen (n i = 6, 5, 4) Balmer Paschen nm E f -E i (J) n i n f 1/n i n i n f 1/n i 0 0 x-intercept 3 3 x-intercept E E E

16 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 R H ) Find relative error in experimental R H Match λ and color to n i and n f Paschen (n f = 3) 5.0E E E-19 y = -4x10-18 x + 6x10-19 R = Not too good E.0E E-19 Slope R H x-int. 1/3 0.0E /n i 16

17 Balmer (n f = ) 5.0E E E-19 y = -x10-18 x + 5x10-19 R = Good: Slope R H E.0E E E /n i x-intercept: 1 ~ 0.5 = so n f = Example Balmer Rydberg Plot Slope (~R H ): J Close to R H J Ef-Ei 6.0E E E E-19 Balmer Series y = -x10-18 x + 6x10-19 R = x-intercept: ~0.4 Close to 0.5 ~1/.0E E E+00 λ (nm) Color λ (nm) E (J) violet E blue-violet E blue-green E red E /n 17

18 Data Balmer color nm E f -E i (J) n i n f red E-19 3 blue-green E-19 4 blue-violet E-19 5 Experimental R H : J Atomic Hydrogen Emission Lines /λ vs. 1/n i cm Lyman Balmer Paschen /n 18

19 Abstract Results Report a: Calibration data and plot b: Table Series plot (Balmer plot) depending on your analysis choice R H and error from literature Predicted wavelengths and error Sample calculations of: photon energy and Rydberg slope Discussion/review questions 19