1-7: The Rydberg Equation

When a sample of gas is excited by applying a large alternating electric field, the gas emits light at certain discrete wavelengths. In the late 1800s two scientists, Johann Balmer and Johannes Rydberg, developed an empirical equation that correlated the wavelength of the emitted light for certain gases such as H₂. Later, Niels Bohr’s concept of quantized “jumps” by electrons between orbits was shown to be consistent with the Rydberg equation. In this assignment, you will measure the wavelengths of the lines in the hydrogen emission spectra and then graphically determine the value of the Rydberg constant, R_H.

1. To start this activity, click this link for The Rydberg Equation. The lab will load in a new tab. Click back to this tab to read further instructions and complete the questions below. You can follow along with the instructions below in the Procedures tab in the lab. The Spectrometer will be on the right of the lab table. You can see the hydrogen emission spectra in the Live Data tab of the tray as well as a graph of intensity vs. wavelength (λ).
2. How many distinct lines do you see and what are their colors?

Box 1: Enter your answer as text. This question is not automatically graded.

3. Click on the Visible/Full button below the graph to zoom to only the visible spectrum. If you hover your cursor over a peak, it will identify the wavelength and intensity. Record the wavelengths of the four peaks in the visible hydrogen spectrum in the data table. (Round to whole numbers.)
4. The Rydberg equation has the form `1/lambda=R_H(1/(n_f^2)-1/(n_i^2))`  where `lambda`  is the wavelength in meters, R_H is the Rydberg constant, n_f is the final principal quantum (for the Balmer series, which is in the visible spectrum, n_f = 2), and n_i is the initial principal quantum number (n = 3, 4, 5, 6, . .). Calculate from your experimental data the wavelength in meters and 1/`lambda` in m^-1. Record your answers in the data table.

Note: for the λ(m) and 1/λ columns, enter your answers in scientific notation. Formatted like: 3E5 or 3*10^5.

      Data Table

Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
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Box 2: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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Box 3: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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Box 4: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 5: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 6: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 7: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 8: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 9: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 10: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
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Box 11: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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Box 12: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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5. The formula for the determination of energy is `E=hnu=(hc)/lambda`  where h is Planck’s constant and c is the speed of light.

What is the relationship between wavelength and energy?

Box 1: Enter your answer as letters. Examples: A B C, linear, a cat

6. Of the four measured hydrogen spectrum lines, which line corresponds to the transition n = 3 to n = 2, and from n = 4 to n = 2, and so on from n = 6 to n = 2?

Box 1: Enter your answer as text. This question is not automatically graded.

7. Calculate the value of `(1/(n_f^2)-1/(n_i^2))`  for the transitions n = 6 to n = 2, n = 5 to n = 2, n = 4 to n = 2 and n = 3 to n = 2. Match the values for these transitions and record them with the appropriate reciprocal wavelength in the results table.

           Results Table

Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 2: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 3: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 4: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
Enter DNE for Does Not Exist, oo for Infinity

Box 5: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 6: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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Box 7: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
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Box 8: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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8. The Rydberg equation, `1/lambda=R_H(1/(n_f^2)-1/(n_i^2))`  , is in the form of y = mx + b where 1/`lambda`  corresponds to y, `(1/(n_f^2)-1/(n_i^2))` corresponds to x, and b = 0. If you plot 1/`lambda`  on the y-axis and `(1/(n_f^2)-1/(n_i^2))`  on the x-axis, the resulting slope will be the Rydberg constant, R_H.

      Using a spreadsheet program or a piece of graph paper, plot your experimental data and determine the value of the Rydberg constant. 

R_H=   /m

Box 1: Enter your answer as a decimal or in scientific notation. Example: 3*10^2 = 3 · 10²
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Please attach a copy of your graph from step 8 here.

Box 1: Select a file to upload

Box 1: