Emission Spectral Lines & the Rydberg Formula

So, n2 is 3.In summary, the shortest wavelength of the Lyman series for a triply-ionized beryllium atom is 7.596 nm.
  • #1
ObliviousSage
36
0
FIGURED IT OUT, PLEASE DISREGARD

Homework Statement



Find the shortest wavelength of the Lyman series for a triply-ionized beryllium atom (Be3+). Express your answer in nanometers using four significant digits.

Homework Equations



Rydberg's Formula: 1/[tex]\lambda[/tex]=RZ2(1/n12 - 1/n22)

The Attempt at a Solution



For the Lyman series, n1 is 1.
Since we want the shortest wavelength, we want the smallest n2, which would be 2.
Beryllium's atomic number (Z) is 4.
Rydberg's Constant (R) is 1.097*107.

Thus 1/n12 is 1, and 1/n22 is 1/4, and their difference is 3/4.

3/4 * 1.097*107 * 42 = 131640000

The wavelength is one over that, or approximately 7.59647523549*10-9m.

In nanometers, to 4 significant digits, that's 7.596nm, yet the website insists that's incorrect (I also tried 7.597nm). What am I doing wrong?
 
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  • #2
This always happens, as soon as I finish typing up my question I figure out what I was doing wrong. >_<

I need n2 as large as possible to get the smallest wavelength.
 

FAQ: Emission Spectral Lines & the Rydberg Formula

What are emission spectral lines?

Emission spectral lines refer to the specific wavelengths of light that are emitted when an atom or molecule undergoes a transition from a higher energy state to a lower energy state. These lines are unique for each element and can be used to identify the presence of certain elements in a sample.

How are emission spectral lines produced?

Emission spectral lines are produced when atoms or molecules absorb energy, such as from heat or electricity, and then release that energy in the form of light. This light is emitted at specific wavelengths depending on the energy level of the transition.

3. What is the Rydberg formula?

The Rydberg formula is a mathematical equation that describes the wavelengths of the emission spectral lines for hydrogen atoms. It is given by 1/λ = R(1/n1² - 1/n2²), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are integers representing the energy levels of the transition.

4. How is the Rydberg formula used in spectroscopy?

The Rydberg formula is used in spectroscopy to calculate the wavelengths of emission spectral lines for different elements. By measuring the wavelengths of the emitted light, scientists can determine the energy levels of the transitions and use the Rydberg formula to identify the element present.

5. What is the significance of the Rydberg formula?

The Rydberg formula is significant because it was one of the first successful attempts to explain the behavior of atoms and their emission spectra. It also paved the way for further developments in quantum mechanics and our understanding of the structure of atoms.

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