Lab Report #3 Emission Spectrum of Hydrogen

The Emission Spectrum of Hydrogen

By: Yusuf Waxali

Lab Station #3Lab Partner: John Richter

February 27, 2014

Experiment #3 Emission Spectrum of Hydrogen February 27, 2014

The Emission Spectrum of Hydrogen

Objective

In this lab, students will use a spectrometer with a diffraction grating to observe the

spectrum of hydrogen and predict the value of R. Also, students will observe the

spectrum of Mercury and verify the diffraction grating constant.

Yusuf Waxali • Physics 244 2


Introduction

One topic that is covered in modern physics is the hydrogen atom. One

interesting quality of the hydrogen atom, as well as every other elemental substance, is

that it absorbs and emits light only at specific frequencies. This can be observed in the

emission spectrum of the hydrogen atom. In this lab, students use a spectroscope to

observe the emission spectrum of hydrogen and verify the work of Johann Balmer.

In 1885, Balmer found that the wavelengths at which spectral lines were

observed fell into the following formula:

1/λ=1.097E7 ( 1/4 -1/n2) where n=3,4,5…

This discovery lead to quantum mechanical analysis of the phenomenon which was

ground breaking for the field of modern physics.

This lab allows students to recreate the experiments of Balmer, verifying both the

Rydberg equation as well as the Rydberg constant, R. Then, students will use the

spectrum of the mercury vapor lamp to verify the factory description on the diffraction

grating. This lab helps to better understand this important point in the history of physics.



Results

Data

After setting up the spectroscope in front of the hydrogen lamp, the angles of each of the four colored spectral lines were recorded for both left and right. These ϴ values were used to calculate the wavelength. See Table 1.

Table 1: θ values for each of the four visible spectral lines. Readings taken both left and right of the central line.

After calculating the inverse of the wavelength and the square inverse of the quantum number as shown in the last two rows of Table 1, the data was plotted on a graph of 1/λ vs. 1/nu

2. See Figure 1.

Figure 1: Plot of intensity data for normal incidence configuration. A clear peak at 24⁰ and another less clear peak at 50⁰



After using the graph to obtain the experimental R value, students used this to calculate both the short wavelength limit and the ionization energy and compare them to published values. The results of this calculation are recorded in Table 2.

Table 2: Ionization Energy and Short Wavelength Limit for Hydrogen using experimental and published value for R.

Finally, students then switched over to the mercury lamp in order to test the grating constant on the diffraction grating. Using spectral lines of known wavelength, students recorded ϴ for the spectral lines and verified the grating constant. See Table 3.

Table 3: Verification of Factory Label on Diffraction Grating. Includes experimental values for lines per mm of grating

Yusuf Waxali • Physics 244

Experimental Published % ErrorShort Wavelength Limit 308.18 337 8.5Ionization Energy 3.32E-19 3.03E-19 9.4

Line Color Green Blueλ (Å) 4359 4078Reading(deg)-right 20 15Reading(deg)-left 19 15Difference (=2ϴ) 39 30ϴ deg. 19.5 15sin ϴ 0.334 0.25Grating Constant d (Å) 13058.45 16312Grating lines per mm (experimental) 765.79 613.06Grating lines per mm (manufacturer) 600 600

5


CalculationsPlease see the attached notebook paper with handwritten calculations.

Results

The experimental R value gathered from the plot of the initial Hydrogen lamp

data was 0.012 nm-1, with a published value of 0.01097 nm-1. This yielded a percent

error of 9.3, which is within the uncertainty of measurement.

The average experimental grating constant was 14685.23, which means an

average of 689.425 lines per millimeter. Compared to the labeled 600 lines per

millimeter, the percent error was 14.9. This was just outside the margin of error from

measurements, however it is close to the manufacturer’s label on the diffraction grating.

.



Conclusion

To summarize, students experimentally verified The Rydberg Constant R as well

as the grating constant on the manufacturer’s label for the diffraction grating. The

results were close to the published values, never exceeding 15 percent error.

One possible source of error is light coming sources other than the lamps being

examined on the spectrometer. Also, while the spectrometer is very precise, the

placement of the diffraction grating is not, as it is done by hand. Not placing the grating

perfectly normal to the incident beam of hydrogen light may skew the diffracted rays and

cause incorrect ϴ readings.

Overall, this lab was effective in demonstrating the work of Johann Balmer and

showing how the linear relationship between 1/λ and 1/nu2 can be used to find the value

of the Rydberg constant R. By recreating the ground-breaking experiment from the 19th

century, students were able to observe the spectral lines of hydrogen and mercury and

better understand Physics as a result.


Lab Report #3 Emission Spectrum of Hydrogen

Documents

Transcript of Lab Report #3 Emission Spectrum of Hydrogen