What Is the Value of m in the Balmer Series Equation for Spectroscopy Analysis?

[UrbanXrisis]

In a lab, our class looked at a hydrogen lamp and calculated the wavelengths of the color red, blue and green. I needed to verify that only Balmer lines are visible using the equation:

1/lambda=R(1/m^2)-(1/n^2)

It says that R is Rydbergs constant and I need to find n. It says that m is the proper value for the Balmer series. What is m supposed to be?

 

[Doc Al]

Balmer series: m = 2

The emission spectrum for the hydrogen atom is given by:
$$\frac{1}{\lambda} = R(\frac{1}{m^2} - \frac{1}{n^2})$$
This represents wavelengths emitted when the atom transitions from a higher state (n) to a lower state (m). (n > m) When the lower state is m = 2, the spectrum is called the Balmer series. It has several wavelengths in the visible range.

Several other spectral series have names (after the experimentalists who discovered them). For example: The Lyman series (ultraviolet) come from transitions to the ground state (m = 1) and the Paschen series (infrared) has m = 3.

 

[M98Ranger]

Hi there,

Thank you for sharing your experience with spectroscopy analysis in your lab. It sounds like a fascinating experiment! Based on the equation you mentioned, it appears that you were studying the Balmer series of hydrogen emission lines. The Balmer series is a set of spectral lines that are visible in the visible light range, specifically the red, blue, and green wavelengths that you mentioned. These lines are named after Johann Balmer, a Swiss mathematician who first discovered the relationship between the wavelengths and energy levels of hydrogen atoms.

In the equation, m represents the energy level of the electron in the hydrogen atom. This value can range from 1 to infinity, with 1 being the lowest energy level (closest to the nucleus) and infinity being the highest energy level (farthest from the nucleus). The proper value for m in the Balmer series is 2, which results in the visible wavelengths of red, blue, and green. This means that when m = 2, the equation simplifies to 1/lambda = R(1/2^2) - (1/n^2), where n is the energy level of the electron in the excited state.

By using this equation, you were able to verify that only Balmer lines were visible in the spectrum of the hydrogen lamp. This is because the equation only applies to the Balmer series and not other series of spectral lines. It is a powerful tool in analyzing the emission spectrum of hydrogen and determining the energy levels of its electrons.

I hope this explanation helps clarify the concept of m and the Balmer series in your spectroscopy analysis. Keep up the great work in your lab experiments!