HYDROGEN SPECTRUM = 2

Transcription

1 MP6 OBJECT 3 HYDROGEN SPECTRUM MP6. The object o this experiment is to observe some o the lines in the emission spectrum o hydrogen, and to compare their experimentally determined wavelengths with those predicted by the Bohr model. THEORY Reerences: Sections.8 and 8.3, College Physics, Serway and Vuille According to Niels Bohr s model (93), the hydrogen atom (Z = ) can only exist in discrete energy states whose energies are given by meke e En = 3.6 = ev n where e and m e are the electron charge and mass; k e is the Coulomb constant; ħ is Planck's constant divided by π; and n is the quantum number (n =,, 3,...). When the atom undergoes a transition rom one state (with quantum number n i ) into a dierent state o lower energy (with quantum number n ), it will emit a photon whose energy is m k h = ( e e E ) = i E e Using the relationship between speed, requency, and wavelength, we may write () hc h = () From equations () and (), the wavelength o the emitted photon is given by i.e. where meke e = π c 3 7 = m R n i = R = Rydberg constant = m. The photons produced by all the possible transitions comprise the emission spectrum o the atom. The lines o the spectrum are classiied into several dierent series, according to the quantum number o the inal state. In the present experiment, we are concerned with the Balmer series. (In 885 a Swiss schoolteacher, Johann Balmer, ound an empirical equation that gave the wavelengths o the visible emission lines in the hydrogen spectrum.) The Balmer series is characterized by n =. The quantum number n i o the itial state is thus equal to 3,, 5,.... (3)

2 MP6. The apparatus used to observe the spectrum consists o a hydrogen lamp and a grating spectrometer. A diraction grating (transmission type) is a piece o transparent material (in our case, gelatin stuck onto glass) with very ine, closely spaced rulings or grooves cut or moulded into it. When a monochromatic beam o light is incident on the grating, an intererence pattern is ormed as the beam passes through each o the grooves. The pattern consists o sharp, bright lines (positions o constructive intererence) whose angular positions are determined by d sinθ bright = m () where m is the order o the line (m = 0,,,...); is the wavelength o the light; d is the spacing between rulings on the grating; and θ bright is the deviation angle o the transmitted beam. Rather than speciying the ruling spacing (slit separation) or a grating, the number o rulings per ut distance, k, is oten given. Note that d = (5) k I the ruling spacing is known and the angular position o a spectral line in a known order is measured, the wavelength o the light orming that spectral line can be calculated: d sinθ bright = (6) m I the incident beam is composed o dierent wavelengths, these wavelengths will be separated into distinct lines. adjustable slit light source collimator spectrometer table diraction grating 0th order spectrum (single line) (line pattern is symmetric about 0th order) Figure. Diagram o Apparatus nd order spectrum st order spectrum

3 PROCEDURE 5 A. Theoretical (Do this beore coming to the lab) MP6.3. Starting rom equation (5), derive the equation or the experimental uncertainty in d due to the uncertainty in k.. Starting rom equation (6), derive the equation or the experimental uncertainty in wavelength due to the uncertainties in d and θ. Reer to page xx o the introduction o the lab manual or inormation on handling the sine unction. 3. Using equation (3), calculate the wavelengths o the irst 3 lines o the Balmer series (n = ; n i = 3,, 5). Express the wavelengths in nanometres. ( nm = 0 9 m). Checkpoint ask the TA to check your calculated wavelengths. B. Experimental (reer to the Appendix at the back o the manual or a description o the spectrometer). Turn on the power supply or the hydrogen gas discharge tube. THE POWER SUPPLY OPERATES AT HIGH VOLTAGE DO NOT TOUCH THE ELECTRICAL CONTACTS BETWEEN THE SUPPLY AND THE TUBE.. Record k, the # o lines/mm or your grating. Note that d, the ruling spacing, equals / k. 3. DO NOT ADJUST THE COLLIMATOR OR THE GRATING the grating has been mounted perpendicular to the collimator. Rotate the telescope in-line with the collimator and observe the bright pink line being emitted by the hydrogen source. Lock the telescope. Observe the zeroth order spectrum (the bright pink line occurring in the incident direction). Check the ocusing o the telescope (the edges o the line should be sharp).. Measure and record the angle o the central pink line. Checkpoint ask the TA to check the setup o your spectrometer. 5. Swing the telescope right and locate the three prominent visible lines o the irst order spectrum: a dark violet line, a bright blue-green (turquoise) line, and a bright red line. Record the angular position o each line under the Right Side Angle column in the data table. Note that the verer scale allows angles to be read to 0. accuracy. 6. Repeat step 5 or each line in second order. I you can ind the third order violet and bluegreen lines measure their angular positions as well 7. Swing the telescope let rom the incident direction and again locate the three prominent lines in as many orders as are visible. Record their angular positions under the Let Side Angle column. 8. Return the telescope to the centre (straight-through) position, and re-measure the angle o the central pink line. 9. Calculate d and δd. Checkpoint 3 ask the TA to review your data.

4 6 MP For each line, calculate the dierence in angular positions (θ bright), the deviation angle θ, and the experimental wavelength (equation 6). Also calculate the experimental error in the wavelength. 8. For each colour, average the experimental wavelengths, average the experimental error in the wavelengths, and algebraically compare the average wavelength with the theoretical wavelength. CONCLUSION Checkpoint ask the TA to review your calculations. Discuss the sigicance o the observation o discrete spectral lines in the emission spectrum o hydrogen. SOURCES OF ERROR Checkpoint 5 ask the TA to join your discussion o the Conclusion. Discuss possible eects due to the adjustment o the spectrometer. Discuss possible eects due to the orientation o the grating. Checkpoint 6 ask the TA to join your discussion o the Sources o Error.

5 MP6 DATA & RESULTS 7 HYDROGEN SPECTRUM k = ( ) lines/mm d = ( ) nm Pink line (m = 0) Itial: θ = ( ) Final: θ = ( ) COLOUR m Right Side Angle, θ R ( 0. ) Let Side Angle, θ L ( 0. ) Dierence, θ R θ L (=θ) ( 0. ) θ (=θ/) ( 0.0 ) (nm)