Solving for n_1 and n_2 in Hydrogen Line Spectra

In summary, to solve for n_1 and n_2 (the initial and final quantum numbers) in this problem, we use the Rydberg Equation and the given information of the line spectra for Hydrogen. The equation is \frac {1}{\lambda} = (R_H)(\frac {1}{n^2_2} - \frac {1}{n^2_2}), where \lambda is the wavelength, n_1 and n_2 are the initial and final principal quantum numbers, with the initial one being larger than the final one. By plugging in the known values, we can solve for n_1 and n_2. If there are still unknowns, we can use the selection
  • #1
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I need help on this problem that asks me to solve for [tex]n_1[/tex] and [tex]n_2[/tex] (the initial and final quantum numbers).

This is the given information (the line spectra for Hydrogen):

color red known wavelength: 656.4 nm
color turquoise known wavelength: 486.3 nm
purple wavelength: 434.2 nm
purple wavelength: 410.3 nm

[tex]n_1[/tex] and [tex]n_2[/tex] are unknown for each one.

I've tried using this equation, the Rydberg Equation, to solve for [tex]n_1[/tex] and [tex]n_2[/tex]:

[tex] \frac {1}{\lambda} = (R_H)(\frac {1}{n^2_2} - \frac {1}{n^2_2})[/tex]

where [tex]\lambda[/tex] is the wavelength, [tex]n_1[/tex] and [tex]n_2[/tex] are the initial and final principal quantum numbers, with the initial one being larger than the final one. [tex] R_H[/tex] is Ryberg's constant.

I've plugged in the numbers and (for the color red) I got
[tex]\frac {1}{656.4} = \frac {R_H}{n^2_1} - \frac{R_H}{n^2_2}[/tex]

I still can't find n1 and n2. Am I using the right formula? I just couldn't understand how to solve a problem with 2 variables.
 
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  • #2
Well n2 > n1, so pick n1 = 1, then solve for n2, which must be an integer.

If that doesn't work, then try n1 = 2, and solve for n2.

Alternatively, one can select n1=1, and then using n2 = 2, 3, 4, . . . solve for the wave lengths.

What value is one using for Rydberg's constant.

Try this reference - http://hyperphysics.phy-astr.gsu.edu/Hbase/hyde.html

Hint - the visible lines are in the Balmer series.
 
  • #3
Also, consider the selection rules as well as the determination of the ionization energy.
 

1. What is the significance of solving for n1 and n2 in Hydrogen Line Spectra?

Solving for n1 and n2 in Hydrogen Line Spectra allows scientists to determine the energy levels of the hydrogen atom, which can then be used to understand the atomic structure and behavior of other elements.

2. How do you solve for n1 and n2 in Hydrogen Line Spectra?

There are various mathematical equations and techniques used to solve for n1 and n2 in Hydrogen Line Spectra, such as the Rydberg formula and the Bohr model. These equations take into account the energy levels, wavelength, and frequency of the emitted or absorbed spectral lines.

3. What is the relationship between n1 and n2 in Hydrogen Line Spectra?

The values of n1 and n2 represent the energy levels of the electron in the hydrogen atom. The difference between these two values determines the frequency and wavelength of the spectral line.

4. Can solving for n1 and n2 in Hydrogen Line Spectra be applied to other elements?

Yes, the principles and equations used to solve for n1 and n2 in Hydrogen Line Spectra can be applied to other elements with similar atomic structures. However, the specific values and calculations may differ.

5. What are the practical applications of solving for n1 and n2 in Hydrogen Line Spectra?

Solving for n1 and n2 in Hydrogen Line Spectra can be applied in various fields such as astronomy, chemistry, and spectroscopy. It allows scientists to identify and study the properties and behaviors of different elements and their energy levels.

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