Atomic Spectra of Hydrogen and Mercury

In summary, the conversation discusses a problem involving the Atomic Spectra of Hydrogen and Mercury, specifically calculating m and Rydberg's constant using a spectrometer. The equations used are α1=(θ1+θ2)/2 (1) and α2= | θ1-θ2|/2 (2) for the average angle, and nλ=d(sin(α1)+sin(α2)) (3) for the wavelength. The results for the Hydrogen spectra are given in nm, and the next step is to calculate values for m and then Rydberg's constant. To do this, the hydrogen energy level diagram must be consulted to see the transitions from a m state to n state. Two wavelengths
  • #1
Imagin_e
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Homework Statement


Hi!

I have a a question regarding the Atomic Spectra of Hydrogen and Mercury. My problem involves the value of m and Rydberg's constant. I used a spectrometer for this lab and calculated all the necessary angles.

Homework Equations


See below

The Attempt at a Solution


average angle:
α1=(θ1+θ2)/2 (1) and α2= | θ1-θ2|/2 (2) (I measured the θ values)

The wavelength for every recorded line in the first order (n=1) :
nλ=d(sin(α1)+sin(α2)) (3)

d= line’s width on the diffraction grating in the spectrometer= 600 lines/mm. In order to compute the width of a single line all that is required is to divide this number by 1 (the inverse). n=2 for Hydrogen btw and it's constant. For Mercury, it's n=1,2,3... (or m=b,c,d,e...)

So, I calculated the wavelengths for every color. I also have the θ1 and θ2 values, which I measured.
Below are the results for the Hydrogen spectra (in nm) after using (3):
violet: 432.462
blue(ish): 486.598
Red: 696.906
Violet: 434.462
blue: 486.598
red: 696.906

Next step is to calculate values for m and then calculate Rydberg's constant. I have no idea how to do it, therefore I'm stuck. I assume that Rydberg's constant can be calculated by rearranging the following equation:
1/ λ=RH((1/m2)-(1/n2)) (guessing, might be wrong)

After I have m, I can calculate m for the second line (m=m+1), third (m=m+2) etc. And then Rydberg's constant for each of the m values and wavelengths.
According to my professor, I'll have two unknowns, which is m and R_H. Therefore, I should use two wavelengths (from above) and try to figure this out. If someone can help me with the Hydrogen spectra, I can continue with Mercury's alone.

Thanks!
 
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  • #2
Imagin_e said:
After I have m, I can calculate m for the second line (m=m+1), third (m=m+2) etc. And then Rydberg's constant for each of the m values and wavelengths.
According to my professor, I'll have two unknowns, which is m and R_H. Therefore, I should use two wavelengths (from above) and try to figure this out. If someone can help me with the Hydrogen spectra, I can continue with Mercury's alone.
you will have to consult the hydrogen energy level diagram and see the transitions from a m state to nstate -the wavelength you have measured correspond to specific set of m,n values.
so you take for two wavelengths and can calculate Rydberg constant and check.
 
  • #3
drvrm said:
you will have to consult the hydrogen energy level diagram and see the transitions from a m state to nstate -the wavelength you have measured correspond to specific set of m,n values.
so you take for two wavelengths and can calculate Rydberg constant and check.

Yes, but according to the professor, I need to calculate the m values for each transition as well. I too looked at the diagram and used the m values (that correspond to each color) that was given there, and then continued to calculate Rydberg's constant (for each wavelength) to see how close the values were to the "correct" one. But she wanted me to calculate m, and then the constant. This by comparing two wavelengths and then get the m value for those two. I have no idea how to do that because I don't know which equation to use (or to derive from) :/
 

FAQ: Atomic Spectra of Hydrogen and Mercury

What is the atomic structure of hydrogen and mercury?

The atomic structure of hydrogen and mercury is composed of a nucleus containing protons and neutrons, surrounded by electrons in specific energy levels or shells. Hydrogen has one proton and one electron, while mercury has 80 protons and a varying number of electrons depending on its ionization state.

What is the significance of atomic spectra in studying hydrogen and mercury?

Atomic spectra, or the specific wavelengths of light emitted or absorbed by an atom, can provide valuable information about the energy levels and electronic transitions of hydrogen and mercury. By analyzing the spectral lines, scientists can determine the composition and properties of these elements.

How are the atomic spectra of hydrogen and mercury different?

The atomic spectra of hydrogen and mercury differ in terms of the number and arrangement of spectral lines. Hydrogen has a simple spectrum with only a few distinct lines, while mercury has a more complex spectrum with many closely spaced lines due to its larger number of electrons and energy levels.

How does the Bohr model explain the atomic spectra of hydrogen and mercury?

The Bohr model, which proposes that electrons orbit the nucleus in specific energy levels, can explain the atomic spectra of hydrogen and mercury. When an electron transitions between energy levels, it releases or absorbs energy in the form of light. The specific wavelengths of light correspond to the energy difference between the energy levels, resulting in the observed spectral lines.

What practical applications do the atomic spectra of hydrogen and mercury have?

The atomic spectra of hydrogen and mercury have various practical applications, such as in spectroscopy for identifying and analyzing elements in samples. They also have uses in lighting and display technologies, with mercury being commonly used in fluorescent lamps and hydrogen being used in hydrogen fuel cells for energy production.

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