EXPERIMENT Hydrogen Emission Spectra

PURPOSE In this experiment you will use a simple spectroscope to observe the line spectrum of hydrogen, identify the wavelength of each transition, and determine the corresponding energy levels. You will also show that these wavelengths fit a pattern of energy states described by a simple formula containing a single constant and integer quantum numbers.

BACKGROUND When an electric current is passed through a sample of gas in a sealed tube the energy excites the electrons of the atoms, causing them to jump to higher energy levels, n (high). Then, as the electrons fall back from the higher to lower energy levels, n (low), that energy is emitted as light. When this light is passed through a prism we do not observe a continuous spectrum, but a line spectrum. In other words, only certain wavelengths of light are observed. This observation strongly suggests that the energy absorbed/emitted by an electron is quantized, or restricted to certain discreet values. Each line in the spectrum corresponds to a particular electronic transition between discreet energy levels. For the emission

Figures 1- A simple spectroscope on the right and on the left “Electron transitions for the Hydrogen atom” is shown along with corresponding wavelengths for the visible region. Note that transition between any pair of states such that ni > nf produces a photon; however, only those transition with nf = 2 and ni= 3, 4, 5, or 6, happen to produce photons in visible range wavelengths. Energy (ΔE) for these transitions can be calculated: (ΔE = − [ Ef − Ei]).

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In this lab, by using a simple spectroscope, at first you will construct a calibration graph using four emissions in atomic spectrum of mercury. In the second part you will measure the position of four lines in the atomic spectrum of hydrogen. The only lines you will be able to observe are those of the Balmer series, visible region of spectrum between 400 and 700 nm. The lines of the Balmer series are the lines for which n (lower), is equal to 2 (i.e. n (low) = 2). Other transitions show up in other regions of the electromagnetic spectrum. For example, all transitions with n (low) = 1 fall in the UV region of the spectrum, while all transitions with n (low) = 3 fall in the infrared. With different detection equipment we could observe those transitions as well.

Once you have identified the transition of each line according to the observed color using figure 1, you will be able determine the corresponding wavelength, λ using calibration graph. Then you could calculate the Rydberg’s constant using the Rydberg equation (below). In other words, given that n (low or final) = 2 (true for all lines in the visible region), you can determine the n (high or initial), and subsequently the energy level from which the "excited" electron came down from.

It is important to note that Rydberg constant is in SI unit “reciprocal meter (m-1)” and represent a 1 limiting value of the highest wavenumber ( ) of a photon that can be emitted from the hydrogen 휆 atom or, alternatively, the wavenumber of the lowest –energy photon capable of ionizing the hydrogen atom from its ground state.

Rydberg’s equation & wavelength Rydberg’s equation & energy 1 1 1 ℎ푐 1 1 = 푅 ( − ) ∆퐸 = ℎ푣 = = −푅퐻ℎ푐 ( 2 − 2) 퐻 2 2 휆 푛푓 푛푖 휆 푛푓 푛𝑖

ℎ푐 1 1 1 7 −1 1 1 −18 = 1.096776 × 10 푚 ( − ) ∆퐸 = ℎ푣 = = −2.179 × 10 퐽 ( 2 − 2) 휆 푛2 푛2 휆 푛푓 푛푖 푓 𝑖

Note: Rydberg's Constant is 1.096776 x 10 7 m-1 which is a distance. Some internet sites say that Rydberg's constant is equal to 2.17869 x 10 -18 Joules but this is not correct. They are using the constant that is derived and is equal to (RH) times (h) times (c).

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Name ______LAB Atomic Emission Spectrum REPORT Section ______Date ______

Instructor ______

Part I: Calibration of the spectroscope (a) Measure the position of the four observed lines corresponding to the known wavelengths by examining the mercury spectrum and enter the result in the table below.

Observed line Positions Color Known Wavelengths (nm) recorded to the nearest 0.1 cm Violet 404.7 Blue 435.8 Green 546.1 Yellow 579.0

(b) Describe any other lines that do not correspond to the known wavelengths.

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Name ______LAB Atomic Emission Spectrum REPORT Section ______Date ______

Instructor ______Part II: Observation and measurement of the hydrogen spectrum: (a) Exam the hydrogen spectrum and enter the observed line positions in the table below and then determine the corresponding wavelengths using the mercury calibration graph.

Observed line Wavelength form the Known Percentage Color position (cm)* calibration graph wavelength (nm) error (nm) Red 656.43 Greenish Blue 486.26 Bluish Violet 434.16 Purple 410.28 *recorded to the nearest 0.1 cm (b) Calculate the corresponding energy per phone (kJ/photon) for each calibrated wavelength and then calculate the corresponding energy (kJ/mol) per mole by using Avogadro’s number.

(c) Using Figure1 determines the values of quantum numbers n1 and n2 for the initial and final states of the transitions that give rise to each line.

Wavelength from the Photon energy Value of ni Value of nf calibration graph (nm) (kJ/mol) (initial state) (final state)

(d) Using the equations provided, calculate the value of the Rydberg constant for each wavelength value in part (c). Enter these values in the table in part e) below. Give one example to show your method of calculation.

(e) Look up the reported value of RH______. Compute your percentage error for determination.

Wavelength from the Experimental value of RH Percentage error calibration graph (nm)

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Name ______LAB Atomic Emission Spectrum REPORT Section ______Date ______

Questions Instructor ______1. Using the Bohr equation, show that the energy of the transition from the lowest (ground) state (n1 = 1) to the highest energy state (n2 = ∞) is given by ∆E (kJ/mol ) = -RH (hc), the derivative of Rydberg constant in terms of Planck’s constant and speed of light. Therefore, the magnitude of this constant is equal to the ionization energy of one mole of hydrogen atoms, in units of kJ/mol.

2. How many emission are possible when hydrogen atom spectra in exited state return to lower energy state and ultimately ground state for emission spectral lines when a hydrogen atom’s electron in the n = 4 quantum level of a Bohr atom drops to the ground state (i.e. n = 1)? Use a diagram to illustrate each of the possible transitions responsible for the spectral lines.

3. Use the Rydberg equation to calculate the wavelength in nm of the light emitted when the electron in a hydrogen atom undergoes a transition from n = 6 to n = 2. Consult figure1 to determine the color of light emitted.

4. Calculate the energy in units of Joules for each photon of light in question above.

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