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Hydrogen and Deuterium Spectroscopy

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Hydrogen and Deuterium Spectroscopy Hydrogen and Deuterium Spectroscopy Abstract: An optical spectrometer equipped with calibrated transmission 0.9 5.00E-04 Reflection Grating Calibration: Using the same mercury discharge tube as sin(theta)versus m x lambda for Hg calibration residual versus m x lambda 4.00E-04 and reflection diffraction gratings with 602.9(2) and 620.1(1) lines/mm, 0.8 of transmission grating for the transmission grating, the positions of 19 Hg emission lines were 3.00E-04 0.7 measured up to 5th order (Figure 3). Using the known wavelengths of the ) respectively, has been used to determine a value for the Rydberg constant. a 2.00E-04 t e h t ) 0.6 ( a n t 1.00E-04 mercury lines, the line density of the grating was determined to be i e Using the transmission grating, the angular positions of 7 Balmer emission s h t n ( i n l i 0.00E+00 0.5 a s u 620.1(1)lines/mm. lines from hydrogen were measured and from a least-squares fit to the data, R d i s -1.00E-04 e 7 -1 0.4 r was determined to be 1.09755(8)´10 m . Using the reflection grating, 26 -2.00E-04 0.3 Rydberg Constant of Hydrogen: Using the calibrated transmission grating, Balmer lines up to 5th order could be observed. From a least-squares fit to -3.00E-04 7 -1 0.2 -4.00E-04 the positions of the violet, green and red Balmer lines from a hydrogen their positions, R was determined to be 1.09819(14)´10 m . Using the same 3.00E-07 5.00E-07 7.00E-07 9.00E-07 1.10E-06 1.30E-06 1.50E-06 3.00E-07 5.00E-07 7.00E-07 9.00E-07 1.10E-06 1.30E-06 1.50E-06 m x lambda (m) reflection grating and a discharge tube containing both hydrogen and m x lambda (m) discharge tube were measured up to 5th order. The angular positions were deuterium, the ratio of the mass of the proton to the electron was determined Figure 1: Plot and LS fit to the calibration data for the transmission grating. The error bars are smaller measured both left and right of the zeroth order position, and, in all cases, the than the symbols used to plot the data. The right-hand graph shows a plot of the residuals from the fit. from the angular splitting of the H and D lines. The relative mass was two angles were the same to within 0.02°. After averaging the two angles, the determined to be 1200(400). wavelengths of the emission lines in each order were determined as: 5.2E+06 2.5E+03 order *1/lambda versus order *(1/4-1/n^2) for Residual in 1/lambda versus order *(1/4-1/n^2) 4.7E+06 hydrogen with reflection grating 2.0E+03 for hydrogen with reflection grating order 123 4 5 Transmission Grating Calibration: To calibrate the transmission grating, Violet 2nd order 1.5E+03 4.2E+06 ) Green 1 violet 433.6(5) 433.8(5) 433.6(3) 433.6(2) 433.73(13) - ) ^ 1 the angular positions of the four prominent emission lines from a Hg - 1.0E+03 m ^ 3.7E+06 ( m a ( d green 485.9(5) 485.5(3) 485.67(16) 485.76(11) 485.70(8) a b 5.0E+02 d m discharge tube were measured in first, second and third order both left and b 3.2E+06 a l m / a 1 l / 0.0E+00 red 655.8(5) 655.9(2) 655.58(15) 655.75(11) not obs n 1 Red i * 2.7E+06 l right of the straight-through position. The angular positions were as follows: r a e Violet u -5.0E+02 d d r s i o 2.2E+06 Green e R -1.0E+03 2 order(m) qLeft(±0.01°) qRight(±0.01°) qMean(±0.01°) Red 1.7E+06 1st order From a least squares fit of 1/l versus (1/4-1/n ), Figure 4, constraining the violet 1 15.23° 15.21° 15.22° -1.5E+03 1.2E+06 -2.0E+03 fitted line to pass through the origin, the value of R for the transmission green 1 19.23° 19.20° 19.21° 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 0.11 0.16 0.21 0.26 0.31 0.36 0.41 0.46 7 -1 yellow 1 1 20.36° 20.35° 20.35° order *(1/4-1/n^2) order *(1/4-1/n^2) grating was 1.09819(14)´10 m yellow2 1 20.43° 20.41° 20.42° 2 violet 2 31.68° 31.68° 31.68° Figure 2: Plot of the measured wavelengths of the H emission lines versus (1/4–1/n ). To separate the green 2 41.15° 41.17° 41.16° different orders, both x and y coordinates have been multiplied by the order of the emission line. The error Measuring m /m using a Deuterium Discharge Tube: Because of the yellow 1 2 44.04° 44.07° 44.05° bars are smaller than the symbols used to plot the data. The right-hand graph shows a plot of the residuals pe yellow2 2 44.25° 44.27° 44.26° from the fit. different masses of the hydrogen and deuterium nuclei, the Balmer emission violet 3 not obs 52.04° 52.04° lines from deuterium are at slightly shorter wavelengths than those from 1 5.E-04 sin(alpha) versus m x lambda for Hg calibration Residual in sin(alpha) versus m x lambda hydrogen. The wavelength difference is related to m /m by: 0.9 4.E-04 pe of reflection grating Using the literature values of the emission line wavelengths, a plot of sinq 0.8 3.E-04 ) 2.E-04 0.7 a æ1+ m / 2m ö against ml gave a straight line (Figure 1), the gradient of which was equal to h l R e p p D H l a ç ÷ ) 0.6 1.E-04 ( a = = »1- m / 2m n h i e p p s the line density of the grating. A least-squares fit the data using LINEST gave l 0.E+00 ç ÷ a 0.5 n ( i l R 1+ m / m l H D e p n i a è ø s -1.E-04 0.4 u d the line density as 602.9(2)lines/mm. i s 0.3 e -2.E-04 R 0.2 -3.E-04 lD - lH Dl Rydberg Constant: Using the calibrated transmission grating, the angular 0.1 -4.E-04 Hence = = -me / 2mp 0 -5.E-04 lH lH positions of the violet, green and red Balmer lines from a hydrogen emission 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 0.00E+00 5.00E-07 1.00E-06 1.50E-06 2.00E-06 2.50E-06 3.00E-06 tube were measured in first and second order. The wavelengths of these lines m x lambda (m) m x lambda (m) were then determined using the diffraction equation for normal incidence Figure 3: Plot and LS fit to the calibration data for the reflection grating. The error bars are smaller than The angular splitting for 4 Balmer lines from a hydrogen/deuterium tube the symbols used to plot the data. The right-hand graph shows a plot of the residuals from the fit. ml = d sinq were measured in third, fourth and fifth order. Each line was measured both left and right of the zeroth order position, and, in all cases, the two angles 1st order 2nd order 1.30E+07 5.00E+03 order/lambda versus order*(1/4-1.n^2) for hydrogen Residual in order/lambda versus order*(1/4-1.n^2) for were the same to within 0.01°. 4.00E+03 with reflection grating hydrogen with reflection grating The measured wavelengths were violet 433.8(3)nm 433.9(2)nm 1.10E+07 3.00E+03 ) 1 - ^ green 485.9(3)nm 486.0(2)nm ) 2.00E+03 1 9.00E+06 m - ( ^ a The wavelengths of the 4 lines, and their wavelength splittings ,were: m d ( 1.00E+03 b red 655.8(3)nm 656.1(2)nm a m d a 7.00E+06 l b / r 0.00E+00 e m llDHDl d a l r 0.1 0.3 0.5 0.7 0.9 1.1 / o r e -1.00E+03 n i d 5.00E+06 r l a o red (3rd order) 655.69(11)nm 655.40(15)nm –0.29(19)nm u -2.00E+03 d The wavelengths of these lines are predicted by the Rydberg equation i s e 3.00E+06 R -3.00E+03 red (4th order) 655.74(11)nm 655.50(11)nm –0.24(15)nm 1 æ 1 1 ö -4.00E+03 1.00E+06 green (4th order) 485.68(11)nm 485.46(11)nm –0.22(16)nm = Rç - ÷ -5.00E+03 2 2 0.1 0.3 0.5 0.7 0.9 1.1 l è 2 n ø order * (1/4-1/n^2) order * (1/4-1/n^2) green (5th order) 485.73(8)nm 485.54(8)nm –0.19(12)nm 2 A plot of 1/l versus (1/4-1/n ) is shown in Figure 2.
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