The Rydberg Equation an Atomic Emission Spectra Activity Worksheet PDF

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Lab worksheet for CH 227. I got a 100% on this lab worksheet. Goodluck! Hope this helps someone taking the course....

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Part A, Determination of the Rydberg Constant 1. From the Beyond Labz portal, start Chemistry in the Quantum Lab.

2. From the presets tab, scroll down and select “Photoemission of H 2 Gas”. The link will take you to a lab table. The Spectrometer will be on the right of the lab table. The center of the table has a gas discharge tube containing hydrogen gas. The hydrogen emission spectra is displayed in the window in the upper right corner (shown as a graph of intensity vs. wavelength). The colors of the corresponding peaks are shown in the window above the spectra. 3. Click on the Visible/Full switch to magnify only the visible spectrum. You will see four peaks in the spectrum, but may only be able to see the corresponding colors of three of them if your eyes are like the authors. If you drag your cursor over a peak, it will identify the wavelength (in nm) in the x-coordinate field in the bottom right corner of the detector window. You can also use the cursor to select a region of the spectra to zoom-in on. You can reset the zoom feature by toggling the visible/full switch. 4. Record the colors and wavelengths of the four peaks in the visible hydrogen spectrum in the Table 1. (Round wavelength values to whole numbers). Even if you are unable to visibly see the fourth peak, the spectrometer can detect it, you can just describe the peak by its wavelength. 5. Convert the wavelength to units of meters and enter in Table 1. ℎ𝑐

6. The formula for the determination of the energy of light is E = where h is Planck’s 𝜆 constant and c is the speed of light. Calculate the energy of each photon (J) and input that value in Table 1. What is the relationship between wavelength and energy? - The shorter a wavelength is, the more energy it will emit/absorb. In contrast, longer wavelengths emit/absorb less energy.

Table 1. Spectrum of Hydrogen Gas Gas:: The observed color and wavelength of each spectra line for 𝒉𝒄 hydrogen gas. The energy of each liline ne was calculate calculated d usi using ng the formula: 𝑬 = color

Line #1 (left most) Line # 2 Line #3 Line #4 (right most)

Dark purple Dark blue Green Red

Wavelength (nm) 410 nm 434 nm 486 nm 656 nm

Wavelength (m) 4.10 4.34 4.86 6.56

× × × ×

10−7 m 10−7 m 10−7 m 10−7 m

𝝀

Energy (J) 4.84 × 10−19 J 4.58 × 10−19 J 4.09 × 10−19 J 3.03 × 10−19 J

7. Compare the energy values from Table 1. The greater the energy of the photon, the greater the value of ni associated with the transition. Given that in the Balmer series n f is always 2, assign an energy and wavelength (m) to each of the corresponding transitions in Table 2. Table 2. The Energies aand nd W Wavelengths avelengths of Transitions: The cal calculated culated energy/wavelength val values ues from Table 1 above were assigned to a transition depending on the amount. The highest energy and wa wavelen velen velength gth values correspond to tthe he hi highes ghes ghestt en energy ergy transition. The lowest energy and wavelengt wavelength h values corr correspond espond to the lowest ene energy rgy transition. Transition ni to nf

Energy (J)

Wavelength (m)

6 – 2 (highest energy)

4.84 × 10−19 J

4.10 × 10−7 m

5–2

4.58 × 10−19 J

4.34 × 10−7 m

4–2

4.09 × 10−19 J

4.86 × 10−7 m

3 – 2 (lowest energy)

3.03 × 10−19 J

6.56 × 10−7 m

8. Calculate the value of (

1

𝑛𝑓2

−

1 ) 𝑛𝑖2

for each of the transitions and input those values in Table 3.

For the wavelength associated with each transition, calculate the inverse wavelength, 1/ (mand input that date into Table 3.

1)

1

Table 3. Transition Values and Inverse Wavelengths: The calculati calculations ons for(𝑛2 − 𝑓

1

𝑛𝑖2

) and the

corresponding inverse wavelength values. These values will ultimately be used to find the Rydberg constant. 1 1 ( 2 − 2) Transition ni to nf 1/ (m-1) 𝑛𝑓 𝑛𝑖 0.222… 2439024.39024 6 – 2 (highest energy) 5–2 4–2 3 – 2 (lowest energy) 1

1

9. The Rydberg equation,  = 𝑅H (𝑛2 − 1

corresponds to y, (𝑛2 − 1

(𝑛 2 − 𝑓

1

𝑛𝑖2

𝑓

1

𝑛𝑖2

𝑓

0.210…

2304147.46544

0.188…

2057613.16872

0.139…

1522070.01522

1

𝑛2𝑖

), is in the form of y = mx + b, where 1/

) corresponds to x , and b = 0. If you plot 1/ on the y-axis and

) on the x-axis, the resulting slope will be the Rydberg constant, RH. Using Excel or

its equivalent, plot your experimental data and determine the value of the Rydberg constant. Copy and paste your graph here (make sure your graph has a title and labeled axis).Use the line of best fit to determine the slope and thus RH and report that vale below with correct units.

Inverse Wavelength's Relation to (1/(𝑛𝑓^2 )− 1/(𝑛𝑖^2 )) 2500000 y = 1.1E+07x - 13855

Inverse wavelength (1/^ (m^-1)

2400000 2300000 2200000

2100000 2000000 1900000 1800000 1700000 1600000 1500000 0.139

0.149

0.159

0.169

0.179

0.189

(1/(𝑛𝑓^2 )− 1/(𝑛𝑖^2 ))

RH = 1.1 × 107 𝑚−1

0.199

0.209

0.219

0.229

The accepted value for RH is 1.0974107 m-1. Determine the % error using the formula:

|1.1 𝑥 107 − 1.0974 𝑥 107 |

× 100 % Error = 1.0974 𝑥 107 % Error = 0.23692%

Part B, Emission Spectra of Other Elements Now, investigate the emission spectra for a different element, helium. Helium is the next element after hydrogen on the periodic table and has two electrons. 1. To exchange gas samples, click and drag the Electric Field and place it on the stockroom counter in the “modifiers” section, and drag the Gas (H2) sample tube and place it on the stockroom counter in the “samples” section. You may have to first click on the main laboratory window in order to move the items. 2. Enter the stockroom by clicking in the Stockroom. Click on the Gases samples on the top shelf. Click on the cylinder labeled He to replace the H2 in the sample tube with helium gas. If you point to the gas sample tube with the cursor it should read He. 3. Return to the laboratory and drag the gas sample tube off the stockroom counter and place it in the middle of the table as indicated by the spotlight. Drag the Electric Field and place it on the gas sample tube. Carefully click the button just above the left zero on the Electric Field controller and change the voltage to 300 V. Turn on the Spectrometer by clicking on the red/green button and click the Visible/Full switch to view only the visible spectrum. 4. Is this spectrum different than hydrogen? How many lines are present and what are their colors? 10. Determine the wavelength (in nm), the frequency (in 1/s) and the energy (in J) for the visible peak on the far right. Table 4: Helium Emission Spectra Color of visible line Wavelength (nm) (far right) Red 668 nm

Frequency (s-1)

Energy (J)

4.49 × 1014 𝑠−1

2.97 × 10−19 J

5. You are encouraged to look at other spectra as well, the writers favorite is mercury.

There is not a formal lab report for this lab. Complete the above pages using the Microsoft version of this file that is available for download on the lab D2L page. Once the worksheet is complete save as a .pdf and submit the worksheet on time and to your TA in the dropbox on D2L....